COVER PAGE
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Excel
TUTORIAL
©2003 and beyond, Lawrence Morales
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Intentionally blank for double-sided copies.
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TABLE OF CONTENTS
COVER PAGE ................................................................................................................................................................. 1
TABLE OF CONTENTS ................................................................................................................................................. 3
BASIC EXCEL FACTS AND USAGE........................................................................................................................... 5
BASIC INTRODUCTIONS TO A SPREADSHEET ................................................................................................................... 5
ENTERING DATA............................................................................................................................................................. 6
EDITING CELL CONTENTS............................................................................................................................................... 8
Changing Cell Formats............................................................................................................................................. 8
Changing Row and Column Sizes ........................................................................................................................... 13
Changing Cell Contents.......................................................................................................................................... 14
WORKING WITH FORMULAS ......................................................................................................................................... 14
COPYING FORMULAS .................................................................................................................................................... 15
ABSOLUTE REFERENCES ............................................................................................................................................... 19
SORTING DATA ............................................................................................................................................................. 21
BASIC MATHEMATICS COMPUTATIONS ............................................................................................................ 29
BASIC MATHEMATICAL FUNCTIONS ............................................................................................................................. 29
Addition................................................................................................................................................................... 29
Subtraction.............................................................................................................................................................. 30
Multiplication.......................................................................................................................................................... 31
Division................................................................................................................................................................... 31
Powers and Exponents............................................................................................................................................ 32
The Natural Base, e................................................................................................................................................. 33
Square Roots ........................................................................................................................................................... 34
The Natural Logarithm ........................................................................................................................................... 35
The Value of π ......................................................................................................................................................... 35
Rounding................................................................................................................................................................. 35
Rounding Up and Rounding Down ......................................................................................................................... 36
BASIC STATISTICAL FUNCTIONS ................................................................................................................................... 37
Averages and Means ............................................................................................................................................... 37
Sums........................................................................................................................................................................ 37
Minimums................................................................................................................................................................ 38
Maximums............................................................................................................................................................... 38
The Range ............................................................................................................................................................... 38
DATABASES .................................................................................................................................................................. 39
BASIC INTRODUCTION TO DATABASES ......................................................................................................................... 39
THE DCOUNT COMMAND ........................................................................................................................................... 40
THE DAVERAGE, DSUM, DMIN, DMAX COMMANDS ............................................................................................ 44
SPECIAL EXCEL FUNCTIONS.................................................................................................................................. 46
THE COUNT COMMAND .............................................................................................................................................. 46
THE COUNTIF COMMAND ........................................................................................................................................... 47
THE RAND COMMAND ................................................................................................................................................. 49
THE RANDBETWEEN COMMAND .............................................................................................................................. 50
THE IF COMMAND ........................................................................................................................................................ 51
THE VLOOKUP COMMAND ......................................................................................................................................... 57
THE HLOOKUP COMMAND ......................................................................................................................................... 59
THE INDEX COMMAND................................................................................................................................................ 60
OPTIONAL: HOW I BUILT THE PHONE LOG FILE ........................................................................................................... 63
GRAPHING .................................................................................................................................................................... 64
BASIC GRAPHING ......................................................................................................................................................... 64
GRAPHING FUNCTIONS ................................................................................................................................................. 78
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GRAPHING HISTOGRAMS .............................................................................................................................................. 83
Bins and Midpoints ................................................................................................................................................. 86
Frequency Command .............................................................................................................................................. 89
Formatting the Histogram ...................................................................................................................................... 90
TRENDLINES ................................................................................................................................................................ 98
THE LINEST COMMAND ............................................................................................................................................ 102
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Basic Excel Facts and Usage
Basic Introductions to a Spreadsheet
A spreadsheet is a software tool that allows you to work with data (mainly numerical) in very
complex and helpful ways. In MATH116 and MATH&148, Excel will be used extensively to
complete the projects in each of the course. Hence, it is crucial that you have a basic understanding
of how spreadsheets work. Here is a basic screen shot of Excel. Please take time to read the callouts
to learn some basic spreadsheet vocabulary.
Clicking on a tab on the Ribbon
This region is called the
brings up groups of commands
Ribbon.
related to each other.
This is the formula bar where
you enter and edit formulas.
The Address Box
tells you what cell
is currently active.
You can enter in a
cell address to go
to directly to a cell,
or use it to give a
cell a specific
name.
Each of these boxes is called a “Cell.” Cells contain,
numbers, text, formulas, or even pictures. A cell’s
address is given by the intersection of the column letter
and the row number. This particular cell’s address is
B3. When you click on or move to a cell, its border
will become highlighted, as shown here.
These tabs select Sheets that you can work in. The current sheet being
worked in is in bold letters. This class will often use files with several sheets
included so pay attention to whether or not these are labeled or named to
indicate more than one sheet exists.
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A spreadsheet may be used to quickly process numerical data, like the simple sales tax sheet shown
below:
Or, they could be used to simulate complex random sampling situations for complicated and
intricate mathematically based problems, such as those we will encounter in MATH116 and
MATH&148.
Entering Data
Entering data into a spreadsheet is as simple as clicking once on a cell and entering the data. You
can also use the arrow keys on your keyboard to navigate to a cell. The active cell will be
highlighted and its address will appear in the Address Box. If you have not opened up Excel yet,
please do so now by opening the file, Blank.xls. Practice moving around the cells if you are new to
a spreadsheet. (In this tutorial, any text that is blue and underlined is a link to an existing file. To
open the link, click on it. If that does not work, try to hold down the Ctrl button on your keyboard
while you click once on a link.)
The simplest kind of data to input is text and numbers.
Practice
Open Navigate to Cell A1 and type in the words “Tax Rate” followed by the Enter key. In
Cell B1, type in the number .0865 (which corresponds to 8.65%). Continue to edit your
worksheet until it looks like this…
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Your entry into cell B2 may not look like a percent when you entered in .0865. To covert a
cell to percent form, choose the cell and the click on the percent button on the toolbar:
In cells A4, A5, etc, enter in a series of numbers. If you want, you can just copy the numbers
you see above. You will probably notice that the numbers you enter are not in dollar format.
To format a group of cells in dollar form, move your mouse to the starting cell (A4 in this
example) and hold the mouse button down while you drag to the last cell you want to
format. It should look like this:
You can then format all of the highlighted cells by clicking on the Dollar format button,
shown below:
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Editing Cell Contents
To edit or change the contents of a cell, navigate to that cell. You will notice that the Formula bar
changes to reflect the contents of the active cell. To edit the contents of that cell, simply use your
mouse button to click in side the Formula bar and edit it as you like. Try in now if you
like…change the value of Cell A7, for example, from 8 to 3.
Changing Cell Formats
There are a variety of different formatting changes you can make to a cell. Here’s a quick rundown
of important formatting tools. (Your tool bar may look a little different than the one shown here, but
the buttons all do the same thing.) For more information, read on in this section:
Change font size
Change
font and
styles
Change font color
Change cell
border
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Format as money
Change
cell
alignment
Format as percent
Merge two or
more cells.
You can make text Bold, Italicized, or Underlined using the formatting buttons shown below:
You can also center text within a cell, or align it to the right or left of a cell with these buttons:
One handy feature of Excel allows you to merge two or more cells into one larger cell. This is
helpful when you are formatting spreadsheet so that they look more professional. For example, in
the sheet below, Cells A1, B1 and C1 have been merged into one large cell:
To merge cells, use the mouse to click and drag all the cells you want to merge. Then click the
Merge button, as shown below:
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To change the font or size of a cell’s contents, use the font formatting tools, shown below:
You can also change the color of the text or data inside a cell. Simply use the Font Color button, as
shown below:
Another nice feature is the ability to add solid borders to cells so that when the sheet is printed, the
borders show up. (By default, the grey cell borders you see while working in a spreadsheet do not
print.) Borders can be added using the border tool:
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As you can see, there are a variety of border options available. Experiment with them to see how
they work…they are pretty straightforward.
Finally, you will often want to format each cell in terms of decimal places, dollar signs, date
formats, percentage format, etc. To format a cell in a particular way, click on the cell(s) you want to
change and then RIGHT click on the cell with your mouse. Choose the “Format Cells…” command
and you’ll get a box like this.
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The “Number” tab will allow you to specify what kind of data is in that cell or cells. For example, if
you want a number, click on “Number” in the “Category” list:
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The new window will allow you to specify how many decimal places to display and change other
formats. (This screen will not round the data, only change what is seen on the screen!).
The other tabs will allow you to change the fonts, borders, etc. However, it’s usually best to keep
things simple, as this generally means it’s easier to read.
Changing Row and Column Sizes
Changing the size of rows or columns is simple. Move your mouse to the vertical bars that separate
each column (or row) until the arrow cursor changes and looks like this:
Then drag your mouse until the column is as large or small as you like:
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Shortcut: If you want to make a column or row automatically size itself to fit its contents, click
once on the row or column label (the numbers 1,2,3,… or the letters A, B, C,…) and then
DOUBLE−CLICK on the vertical bar directly to the right or below the column or row you want to
resize.
Changing Cell Contents
There are a variety of different
Working with Formulas
Working with simple formulas in Excel is as easy as using an “=” sign and typing in the formula
correctly. One of the most common calculations is to take numbers in two or more different cells
and compute with them.
Practice
Open the file called Formulas.xls. Make sure you are on the Sheet called “Copy Down”
before proceeding. You will see two columns of numbers. In Cell C2, type in the word
“Sum.”
We are going to add the two numbers in each row and put the result in Column C.
In Cell C3 type the following:
=A3+B3
followed by the Enter key. You should see the number 13 appear in Cell C3.
Note that Cell C3 tell Excel to take whatever is in Cell A3 and add it to whatever is in Cell
B3. This is helpful because if were to change the contents of either A3 or B3, the result
would automatically change in C3. Try it…change A3 and/or B3 to make sure it works.
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Practice
Let’s continue to modify the file called Formulas.xls. In Cell D2, type the word “Product”.
In Cell D3, type the following formula:
=A3*B3
followed by the Enter key. You should see the number 30 appear in D3. This is the product
of the first two numbers on our list.
Copying Formulas
In the previous Practice problems, we’ve managed to compute the sum and product of two numbers.
If we want to duplicate that set of calculations for all of the rows present, we certainly do not want
to have to type formulas into every cell. Instead, we will copy or duplicate the formulas down the
columns in one short set of steps.
Example
Let’s continue to modify the file called Formulas.xls. At this point, it should look like this:
We are going to copy the formula in Cell C3 all the way down to the end of the list of
numbers we have. To do this first click once in Cell C3 and hold the mouse down while you
carefully drag to the end of the list. Your screen should look something like this:
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Now, while you hold the Ctrl button down on the keyboard, hit the D key. This is called a
Ctrl−D command. When you do so, the Cells in Column C should fill themselves in as
below:
Now here is the best part! Click on any of these new cells, such as C4 and look at the
formula bar. You will notice that the original formula you entered into C3 has been copied
but it has been automatically altered to reflect the fact that you are now adding numbers in
Row 4. Excel is smart enough to adjust these new formulas for you so that you get the
results you were actually looking to get.
The original references to A3 and B3 that we entered into Cells C3 and D3 are called
relative references. This means that should we copy the formulas in these cells to other
cells, Excel will assume that we want to copy the formulas so that they adjust, relative to the
original formula.
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Practice
Copy the formula in Cell D3 down to include all the numbers with rows in them. Make sure
each new entry really is the product of the numbers in Columns A and B.
Example
We can also copy a cell’s formula to the right with the Ctrl−R (Control Right) command. In
the Sheet called “Copy Right” in the file Formulas.xls, you will notice numbers in rows,
rather than in columns. Please examine the formulas in Cells B4 and B5.
Now, click on Cell B4 and then hold the mouse button down while you drag over to Cell F4.
Use the keyboard to type a Ctrl−R command (This means hold the Ctrl button down while
you type the letter R.) The formulas should be copied and the calculations down for you so
that the file looks like this:
Practice
Copy the formula in Cell B5 to the right to multiply all the column pairs of numbers.
The Copy Handle
There is one other way to copy formulas to the right, left, down, or up from a cell that
already has a formula in it. In the Sheet called “Copy Handle” in the file Formulas.xls, you
will see a set up as follows:
Click on Cell E4 to see the formula =E3+5. When you click on the cell, you should notice a
small, square handle in the lower right corner of the cell:
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The Copy Handle
I’ll call this the “Copy Handle.” If you click on this handle and hold the mouse button down
while you drag over to cell I4, Excel will copy the formula of E4 across the row. Try it!
You can also click on E4 and drag the Copy Handle down Column E. Try it!
Finally, you can drag the Copy Handle in Cell E3 to the left and it will copy the formula to
the left. I’ve doe this and here is what my sheet looks like now:
You can now click on any cell with a number/formula in it and drag right, left, or down to
fill in formulas. As a matter of fact, you can do it very efficiently. For example, select the
range of cells A4 to I4 as shown below:
Note that this entire range has one Copy Handle associated with it. Grab this handle and
drag down to Cell I9 (or thereabouts) and watch all of the rows fill in nicely:
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This provides a quick and easy way to copy your relative formulas all over a sheet and not
have to type each on in by hand.
Absolute References
Sometimes, you don’t want your formulas copied in a relative way. There may be a particular cell
that you always want to be part of a formula. Excel uses absolute references to accomplish this and
it uses the $ sign inside a Cell address to make the address absolute.
For example, if you always wanted Cell A2 to be used in a calculation, you would need to type in
$A$2 to tell Excel this is an absolute reference. Let’s see how this would work:
Example
Open the Sheet called “Shipping” in the file Formulas.xls. The goal of this example is to
add the Shipping Fee of $8.95 in Cell A2 to every relevant row of the “Total with Shipping”
Column.
To do this, we enter the following into Cell B8:
=A8+$A$2
and then copy this formula down using Ctrl−D. Here is what the results look like:
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Note that we can change the shipping amount in A2 and all the cells in Column B will
update.
Example
Edit the sheet “Shipping” so that in Column C, the “Total with S&H” of each cell adds the
“Order Amount” to the Shipping Fee in A2 and the Handling Fee in Cell A5. Try to use
Copy Down for practice.
Answer:
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There are other variations on using absolute references. For example, you may want a cell to
compute with a particular row but allow the column to be relative (and therefore change) or
vice versa. Here are the three possibilities for absolute or partially absolute references.
Example Type
Comment
$A$2
True absolute reference
Forces computation with Cell A2
$A2
Partial absolute reference Forces computation with Column A but allows
the row number to change relative to the
formula.
A$2
Partial absolute reference Forces computation with Row2 but allows the
Column to change relative to the formula.
Note: If you are editing a formula, using the F4 key will cycle you through different kinds of
absolute references. Just make sure the reference you want to change has the edit cursor
immediately to the left of the reference in the Formula Bar.
Sorting Data
Sorting data sometimes makes it easier to see what is going on. Open the file Employees.xls to see a
series of Sheets with data in them.
The Sheet called “Employees” is a simple list of Employee ID numbers. To sort these in ascending
or descending order, we use the Sort & Filter button on the toolbar.
First, click on Column A so that the entire column is selected. (Click on the box with the A at the
top of the column.) Your column should look like this:
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Now click on the Sort & Filter button and then choose
and the employee number will be sorted
in ascending order. Clicking on the Sort Down button
will sort them in descending order.
Usually, however, you will want to sort more complicated data. Select the Sheet called “Sales
Records” to see data on the employees’ sales records and their time employed at the company.
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Example
We want to sort these records by their Employee number once again, but if we simply sort
what is in Column A, then the records will not match the data that is Columns B and C. To
make sure that all the data is sorted correctly, we first need to select all the rows to be sorted.
Move your mouse to the left side of the screen until the arrow is over the “1” in the box that
identifies Row 1. If you do this correctly, the normal cursor arrow will turn into a heavier
arrow pointed to the right that looks like this:
Click once on the mouse button and drag it down to Row 22, and then release the mouse
button. Your screen should look like this:
All rows should be highlighted. Now you can use the Sort Up or Sort Down Button to sort
by Employee number. Note: Excel will automatically sort the data according the column on
the very left of whatever is highlighted. You can also shift to the Data portion of the Ribbon
and use the Sort buttons there as well:
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If you want to sort by Sales amount, you’ll need to use the Sort command in the Data tab of
the Ribbon:
Example
Let’s sort the Employee data now by Sales. Once again, use the row labels to highlight
Rows 1 to 22. Click on the Sort button in the Data group (see picture above) and you’ll get
this box:
If the “My data has headers” box is checked, then Excel looks at the first row of the data that
is highlighted and treats that as the one that has headers, or descriptors in it. When it sorts
the data, it will leave the header row at the top (as you would want) and sorts everything
below the header row.
This box allows you to specify what to sort by first. The default is the left−most column, but
we can select Sales instead, as below:
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Doing this and clicking OK will sort by Sales from smallest to largest values:
Again, it is vital that all rows and columns be selected so that when the data is sorted, the
Employee number is properly matched up with that person’s sales total and years on the job.
Example
Let’s sort by Years on the job first (ascending), and then by sales (descending). After
selecting all rows, we choose the Sort button and then configure our Sort box as follows.
First, select years on the job as the first sorting criterion:
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Then, we add a level of sorting so we can also sort by Sales. To do this, click the “Add
Level” button:
You can then Choose Sales from the first box and Largest to Smallest from the last box:
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When we click OK, we get the following:
This allows us a view of the data that is perhaps very helpful if we are a manager trying to
determine who the most effective salespeople are.
Practice
Open the file ClassData.xls and sort all records by Student ID (ascending).
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Answer: The first few rows should look like this: (check all the way across the row to make
sure you have it sorted correctly.)
Practice
Open the file ClassData.xls and sort all records by Exam 2 (descending).
Answer: The first few rows should look like this: (check all the way across the row to make
sure you have it sorted correctly.)
Practice
Open the file ClassData.xls and sort all records by Exam 1 (descending) THEN Exam 2
(descending) THEN by Exam 3 (descending).
Answer: The first few rows should look like this: (check all the way across the row to make
sure you have it sorted correctly.)
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Basic Mathematics Computations
There are several special mathematical computations you will need to be able to do in Excel. This
part of the tutorial covers many of these.
The first thing to be aware of when doing any computations in Excel is that you will usually need to
start the contents of a cell with the “=” sign in order for Excel to recognize the formula
computations.
Basic Mathematical Functions
Addition
To add two or more numbers, use the + symbol, as you would normally.
Example
To add 5+3+2 type the following into a cell
=5+3+2
When you hit the Enter key, the cell will change to a 10.
If you want to add numbers that are located in different cells, you need to type in the cell addresses
for each number to be added to the result.
Example
Suppose you wanted to add the values that are in cells A1, A5, and B6 (see below), and you
wanted to place the result in cell C1.
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Type the formula
=A1+A5+B6
in this cell
In cell C1, type the following:
=A1+A5+B6
When you hit the Enter key, cell C1 will display 24.
There is a nice shortcut to typing cell references that can save time. Instead of typing the cell
reference, use the mouse to point and click at the cell you want entered into the equation. In
this example, you can do the following:
Type =
Use the mouse to click once on cell A1
Type +
Use the mouse to click once on cell A5
Type +
Use the mouse to click once on cell B6
Hit the Enter key
Practice
Open the file called BasicMath.xls and use it to add cells A8, B2, and B7. Try to use both
methods described above.
Answer: 17
Subtraction
To subtract numbers, use the − symbol, as you probably suspected.
Example
To compute 20+3−5−8, you would type:
=20+3−5−8
The result will be 10, as it should be.
Practice
Open the file called BasicMath.xls and use it to compute the result of 56+A4−13−B3
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Answer: 46.
Multiplication
To multiply numbers, use the * symbol, which is Shift−8 on the keyboard.
Example
To compute 2 × 3 × 4 , you would type:
=2*3*4
followed by the Enter key.
Practice
Open the file called BasicMath.xls and use it to compute the result of 3*A4*B12
Answer: 210
Example
If you want to use the distributive property of multiplication, you will need to use
parentheses. To compute 5(3 + 2 − 8 + 7) , you would type:
=5*(3+2−8+7)
Notice that you need the * between the 5 and the left parenthesis. Excel will display an error
message without it.
Practice
Open the file called BasicMath.xls and use it to compute the result of 4(6−A10+B5+3).
Answer: 40
Division
To divide two numbers, use the / symbol on the keyboard.
Example
32
To divide , which is the same as 32 ÷ 8 , type:
8
=32/8
followed by the Enter key.
Example
You need to be very careful with division and the order of operations. For example, if you
3+8
want to compute
, you must tell Excel that the 3+8 are to be added before being
4
divided by 4. Hence, to compute this, you would type:
Excel Tutorial - Page 31
=(3+8)/4
followed by the Enter key. The result will be 2.75, which is correct.
Note that if you were to type the following;
=3+8/4
8
then Excel would actually compute 3 + , which is 5, a totally different (and wrong) result.
4
Practice
5+ 6+ 7 +3+ 4+ 6+ 7
.
7
Answer: Approximately 5.428571
Compute
Practice
Open the file called BasicMath.xls and use it to compute the result of
A3 + A2 + B5 + B9
12
Answer: 2.25
Powers and Exponents
If you want to raise numbers to powers, then you need to use the ^ symbol, which is Shift−6 on the
keyboard. If you familiar with a TI graphing calculator, this symbol is the same symbol you used to
compute with powers.
Example
To compute 2 4 , you would type:
=2^4
to get a result of 16
Example
To compute (2 + 5) , you would type:
3
=(2+5)^3
to get a result of 343.
Example
To compute 4(2 + 3)
( 2 +1)
, you would type:
=4*(2+3)^(2+1)
to get a result of 500. Note that if the power is complicated, you may need to use
parentheses to make sure the proper exponent is applied.
Practice
Compute 5 4 .
Answer: 625
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Practice
Compute 2.35 3 .
Answer: 12.97788
Practice
Compute 7 + 2(4 − 3 − 5)
Answer: −121
3
Practice
Open the file called BasicMath.xls and use it to compute the result of 5(B1−A3)5
Answer: -15625
The Natural Base, e
One of the most important bases we apply exponents to is e, the natural base. The value of e is
about 2.72, but Excel knows its exact value, provided you use the EXP() command. If you just use
the letter “e” in the formula, Excel will not recognize it as the natural base.
Example
To compute e1 , which is of course just e, you would type:
=EXP(1)
to get the value of e to however many decimal places Excel is set to display in that cell.
Example
To compute e 5 , you would type:
=EXP(5)
to get a value of 148.4132.
Example
To compute e (1+ 2.35 ) , you would type:
=EXP(1+2.35)
to get a value of 28.50273. Note that you need parentheses around the exponent part.
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Practice
Compute e 5.45 − 3.26 . Don’t forget to use parentheses around the exponent part.
Answer: 8.935213.
Practice
1
( 3− 7 )
Compute e 2
. Don’t forget to use parentheses around the exponent part.
Answer: 0.135335.
If you did not get this, check your entry to make sure it looks like this:
=EXP((1/2)*(3-7))
Make sure you recognize how and why each of the set of parentheses is being used.
Square Roots
The most common root you will need in this course is the square root. To compute a square root,
you can do one of two things: (1) You can raise the base to the power of ½. Recall that taking a
square root is the same as raising a number to the power of ½. (2) You can use the SQRT()
command.
Example
To compute 18 , you can type one of the following:
=18^(1/2)
OR
=SQRT(18)
Notice that in the fist case, parentheses are needed around the ½. This is important! Also, in
the second case, parentheses are needed around whatever is inside the square root symbol.
Example
To compute
5 + 20 , you can type one of the following:
=(5+20)^(1/2)
OR
=SQRT(5+20)
Either one gives you a result of 5.
Practice
Compute the value of 12 + 36 − 15
Answer: 5.744563
Practice
Compute the value of
Answer: 15.75608
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38 + 2 5 + 18
The Natural Logarithm
This course will require that you do limited computations with logarithms. The logarithm we will
use is the natural logarithm, which is symbolized by ln. Excel can compute these easily using the
LN command.
Example
To compute the value of ln(10), you would type:
=LN(10)
to get a value of 2.302585. Note once again that parentheses are needed. Whatever you are
taking the logarithm of needs to be in parentheses.
Example
To compute ln(5 − 8 + 2 × 9) , you would type:
=ln(5−8+2*9)
to get a value of 2.70805.
Practice
Compute the value of ln(44.5)
Answer: 3.795489.
Practice
Open the file called BasicMath.xls and use it to compute the result of 5−ln(B5+A3)
Answer: 2.227411.
The Value of π
The value of π can be easily computed in Excel. Simply type =PI() into a cell or any part of a
formula and the value of π will be invoked. Note that the parentheses are necessary.
Rounding
When you want to round numbers, the ROUND command is used. The syntax is:
=ROUND(value, rounding_parameter)
where value is the number to be rounding, and rounding_parameter is the number of places to
round to.
Example
To round cell A5 to the nearest hundredth (2 decimal places to the right of the decimal
point), you would enter:
=ROUND(A5,2)
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Example
To round cell A5 to the nearest tenth (1 decimal place to the right of the decimal point), you
would enter:
=ROUND(A5,1)
Example
To round cell B10 to the nearest integer (0 places to the right of the decimal point), you
would enter:
=ROUND(B10,0)
Example
To round cell C1 to the nearest ones place, you would enter:
=ROUND(C1,−1)
Note that the rounding parameter is −1, indicating you are rounding to one place to the
LEFT of the decimal place.
Practice
The file SalesTax.xls has a random list of sales prices. In the column titled “Sales Tax,”
compute the sales tax on each item, using the ROUND command to round the tax amount to
the nearest penny. Use absolute references to insure that you use the constant tax rate in Cell
B1. Then fill in the “Total Due” column, which is the sum of the Price and Sales Tax. When
you are done, you should be able to change the value of the tax rate in Cell B1 and see all
your other values change accordingly.
Note that the ROUND command rounds to the nearest place value. That is, it may round up or
round down, depending on the value. If you want to strictly round up the next place or down to the
previous place, then the following commands are used.
Rounding Up and Rounding Down
To round up, we use the ROUNDUP command, which has a similar syntax to ROUND. The
difference is that it will round a value UP. To round down, we use the ROUNDDOWN command,
which has a similar syntax to ROUND. The difference is that it will round a value DOWN
Example
To round the value 345.8768 UP to the thousandths place (3 decimal places), we would
enter:
=ROUNDUP(345.8768,3)
to get a value of 345.877. This is also what you would get if you use the ROUND command.
However….
Excel Tutorial - Page 36
Example
To round the value 345.8768 DOWN to the thousandths place (3 decimal places), we would
enter:
=ROUNDDOWN(345.8768,3)
to get a value of 345.876. This is not what you would get if you use the ROUND command
since this command does not round to the nearest or up, but down to the previous place
specified.
Basic Statistical Functions
Averages and Means
To find the average, or the mean, of a group of numbers, we use the AVERAGE command. The
syntax is:
=AVERAGE(cell_range)
Example
To find the average of the numbers in cells A1 to A50, we would enter:
=AVERAGE(A1:A50)
This is pretty much straightforward. If you have numbers in more than one column, like
from Cell A1 to Cell C20, then you would type:
=AVERAGE(A1:C20)
Practice
Open the file SalesTax.xls and find the average of the Prices listed in Column A. Place your
value in Cell A20.
Answer: $16.52
Sums
To find the sum of a list of numbers, we use the SUM command:
=SUM(cell_range)
Example
To find the sum of the numbers in the block of data from Cell B20 to Cell T55, we would
type:
=SUM(B20:T55)
Practice
Open the file SalesTax.xls and find the sum of the Prices listed in Column A. Place your
value in Cell A21.
Answer: $264.25
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Minimums
To find the minimum number in a list of a block of cells, we use the MIN command:
=MIN(cell-_range)
Example
To find the sum of the numbers in the block of data from Cell B20 to Cell T55, we would
type:
=MIN(B20:T55)
Practice
Open the file GPA.xls and find the minimum GPA listed.
Answer: 0.53
Maximums
To find the maximum number in a list of a block of cells, we use the MAX command:
=MAX(cell_range)
Example
To find the sum of the numbers in the block of data from Cell B20 to Cell T55, we would
type:
=MAX(B20:T55)
Practice
Open the file GPA.xls and find the maximum GPA listed.
Answer: 4.0
The Range
The range of a set of numbers is simply the maximum in the list minus the minimum in the list.
There are two ways to compute the range, therefore. Either (a) compute the MIN and MAX
separately and then subtract them in a third cell. Or (b) use one command to do it in one cell using
the a command like =MAX(cell_range)−MIN(cell_range). Just make sure the cell ranges used in
each of the MIN and MAX command are the same.
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Databases
Basic Introduction to Databases
A database is a large collection of data and records. For example, open the file Chrysler.xls to see a
database that represents the cars sold at a local Chrysler Dealership in the recent past. There are
literally hundreds of records.
Each row represents a different record. In this case, each record represents one individual sale of a
car. Each record in a database is made up of several fields. The fields are the different parts of the
record. In Chrysler.xls, the fields are Car Number, Style, Color, Sale Price, SalesPerson. Each of
these fields has different kinds of values that are possible. For example, the Sale Price field must
take on a number ($) while the Color field takes on text values (such as Red, Blue, etc.)
These are the fields
These are the
records.
Now suppose you wanted to ask questions like: “How many Red PT cruisers have we sold?” or
“How many cars over $25,000 did Juan sell?” or “How many Concordes and Voyagers did we sell
between $20,000 and $23,000?” Trying to do this would take a lot of time and hassle without
special commands like DCOUNT.
When using database commands like these, we need to give the commands specific criteria with
which to work. Hence the first thing to do when using these commands is to duplicate the Field
headings above or to the side of the actual data so that we can enter specific criteria. For example,
we can alter Chrysler.xls as follows: Insert 7 new blank lines above the data. (Select Rows 1 to 7 by
clicking on the Row 1 label and drag down to Row 7, then choose Insert→Rows from the Menus.)
In cell A1, we will type “CRITERIA.” In cells A2 to E2, we will copy the original Field headings.
Our modified worksheet will look like this:
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We will call
this the
Criteria
Area.
We will use cells A3 to E7 to fill in specific criteria. Usually 5 or six lines is enough, but if we need
more, we can always insert new blank lines.
With the Criteria Area now available we can proceed.
The DCOUNT Command
The DCOUNT command simply counts the number of records in a database that meet stated
criteria. We enter the criteria into the Criteria Area and then run the DCOUNT command. This
command uses the syntax:
= DCOUNT(database,field,criteria)
where database is the range of cells where the database is located, field is unused, and criteria is the
range of cells where you specify what criteria to match and therefore which records to count.
Example
Let’s count the number of Red PT Cruisers sold at this dealership. Using Chrysler.xls, we will
modify the Criteria Area so the first line has Red in the Color column and PT Cruiser in the
Style column. It is crucial that we enter the text in without any spelling errors, including any
spaces that are needed. This is how our file should look…try it yourself as we move along:
Let’s use the Function Wizard to invoke the DCOUNT command since it’s easier than using
the syntax.
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First, click on a blank available cell where Excel can report the number of Red PT Cruisers.
Make sure you pick a cell that is not in the Criteria Area or part of the database. Let’s label
Cell G2 as “DCOUNT” first and then use Cell H2 as the cell where we will return DCOUNT
results. Click on Cell H2.
We now use the DCOUNT command to count the number of Red PT Cruisers in the database.
The format for DCOUNT is, as we saw above:
= DCOUNT(database,field,criteria)
In Cell H2, we enter the following command:
The range A7:E537 is our database. Notice it includes row 7 which has the field names of our
database. Also notice that the field parameter is blank. We don’t need it here. Finally, the
range A2:E3 is the criteria range and it includes the row with the field headers and the row
where specify the two criteria. When you use the DCOUNT command, the row with the field
headers MUST be included in BOTH the database range AND the criteria range.
Make sure that the “Criteria” box does not include any of the empty rows in the Criteria
Area….if it does, it will count all 350 cars in the database.
Example
Let’s count the number of PT Cruisers sold at this dealership that are either Red or Black. To
do this, we need to add another line in our Criteria Area as follows:
When there are two or more rows filled out in the Criteria Area, DCOUNT will look for
records that match ANY of the criteria and then add them all up. That is, Excel will look for
any Red PT Cruisers OR any Black PT Cruisers.
Because we changed the criteria, we also need to change the formula in Cell H2 to make sure
it is updated. We could run the DCOUNT Function Wizard all over again, but here’s a nice
shortcut that you can use any time you want to edit a function.
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Click once on Cell H2. Then hit the F2 key on the top row of the keyboard. When you do,
your screen should look like this:
Drag this handle to
change the active Criteria.
This is the Criteria range,
highlighted in green
This is the Database cell
range highlighted in blue
Notice two great things happen. First, the formula in H2 is displayed with colored fonts. The
colors correspond to the colored boxes that are now outlined in blue and green. The database
range is outlined in blue and the Criteria Area is outlined in green. If we want to include Row
4 in the Criteria Range, we can either edit A2:E3 so that it reads A2:E4, or we can simply
point on the little square handle on the lower right corner of the green box (also the lower right
corner of Cell E3 if you can’t see the color) and drag it until it expands to E4. When you do
so, the screen will look like this:
Note that the formula and colored boxes stay synchronized. Very cool!. Now hit the Enter
key and the formula and Cell H2 will be updated. There are 17 PT cruisers sold that were
either Red or Black.
Practice
How many Blue 300M’s were sold?
Answer: 3
Practice
How many Voyagers did Juan sell? What about Maria?
Answer: 12 and 8
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Practice
How many Red Concordes did Bartoloa sell?
Answer: 2
Practice
How many PT Cruisers or Crossfires were sold?
Answer: 118
Practice
How many PT Cruisers or Crossfires were sold by Elias?
Answer: 23
Practice Challenge
How many PT Cruisers or Crossfires were sold by Elias or Juan?
Answer: 43 (Hint: You need four lines filled in your Criteria Area!)
Example
Now, what if we want to count the number of PT Cruisers sold for under $22,000? Our
Criteria Area and results would look as follows:
Example
How many 300M’s were sold for $25,000 or more by Celia? Our Criteria Area and results
would look as follows:
Example
How many Pacifica’s were sold for between $18,000 and $22,000? This is a different
question! We want to count all cars that meet both the >18000 AND <22000 criteria so we
can’t use two different rows in the Criteria Area. (That would count each inequality separately
and then add them, which is not what we want.) Both of the Price criteria have to be in one
row. To accomplish this, we need to insert another column to the Criteria Area and label it
“Sale Price.” We’ll use Column F and enter our criteria, like below. If we make sure the
DCOUNT formula in Cell H2 includes the new Column, our results will be accurate:
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There were 14 Pacifica’s sold for between $18,000 and $22000.
Practice
How many Sebring’s were sold for more than $20,900?
Answer: 19
Practice
How many Town&Country’s were sold for less than $25,000?
Answer: 26
Practice
How many Black 300M’s were sold for more than $23,000?
Answer: 6
Practice
How many Voyagers were sold for between $21,000 and $23,000?
Answer: 11
Practice
How many Sebring’s or PT Cruisers were sold for between $15,000 and $18,000?
Answer: 9
The DAVERAGE, DSUM, DMIN, DMAX Commands
If you have a database and you want to find the averages, sums, minimum or maximum values
subject to given criteria, these commands are the ones to use. They all work very similar to each
other, so we’ll only cover DAVERAGE here. You can explore the rest on your own.
DAVERAGE will find the average of some field in a database subject to your criteria.
Practice
What is the average price of all PT Cruisers sold in Chrysler.xls? We change Cell G2 to say
“DAVERAGE” and use Cell H2 to compute this average. Make sure your Criteria Area looks
like this:
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The command is as follows:
The basic command structure is:
=DAVERAGE(database,field, criteria)
Now, the field criteria IS needed. We specify D7 as the field because that is the field header
for the Sale Price data.
Practice
What is the average price of all of the M300’s sold by either Maria or Celia?
Answer: $23,861.78
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Special Excel Functions
The COUNT command
There are times when you have a long list of data and you want to quickly count how many items
are in the list. The COUNT() command does this quickly.
Open the file Count.xls to see a sheet full of numbers. Note that some of the cells are empty so that
the columns do not necessarily have the same number of entries in them. The syntax for the
COUNT command is:
=COUNT(cell_range)
The COUNT command counts the number of cells in a given range (specified by the cell range)
that contain numbers within them.
Example
If you wanted to count the number of cells with numbers in the Red column, you would type
in Cell A22:
=COUNT(A1:A21)
to get 20 for a result. Note that even though cell A1 is included in the range of cells to be
considered, it is not counted because cell A1 does not have a number inside of it.
Example
If you wanted to count the number of cells with numbers in the Blue column, you would
type in Cell B22:
=COUNT(B2:B21)
to get 17 as a result. Note that I did not include cell B1 in the cell range since I knew it
would not be counted anyway.
Example
If you wanted to count the number of cells with numbers in BOTH the Grey and Black
columns, you would type:
=COUNT(H1:I21)
to get 37 as a result. The range you use can include more than one column.
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Practice
Open the file called Count.xls and use the COUNT command to count the number of cells
in the Pink column with numbers in it.
Answer: 18
Practice
Open the file called Count.xls and use the COUNT command to count the number of cells
in the Green and Brown columns with numbers in them.
Answer: 18
Practice
Open the file called Count.xls and use the COUNT command to count the number of cells
in ALL of the colored columns.
Answer: 164
The COUNTIF command
Sometimes, simply counting is too general. There are times you want to count the number of items
that meet specific criteria. The COUNTIF command will do this for us. The syntax for the
command is:
=COUNTIF(range, criterion)
where the range specifies which cells to count and the criterion details what to look for.
For example, the MachineJams.xls has a list of data a company has been recording for several
months. The copy machine they lease has been jamming regularly, but the company they lease the
machine from says nothing should be wrong with it, since it’s new. So, the company has recorded
the number of times it jams per day to document their experience in case they need to insist that it
be replaced. Each row represents a different day.
What we want to do is count the number of days in which certain criteria are met.
Excel Tutorial - Page 47
Example
Suppose you want to count the number of days during the first 14 days in which there were
more than 10 jams per day. (It is possible to count these with your naked eye, but we will
practice using the COUNTIF.) You would type the following:
=COUNTIF(B2:B15, “>10”)
to get a result of 7. Note that the criteria should be in quotes. (It’s an odd rule, but it exists
nonetheless.)
Example
Suppose you want to count the number of days during the first 20 days in which there less
than or equal to 6 jams per day. You would type:
=COUNTIF(B2:B21,"<=6")
to get a result of 6. Note that ≤ is typed as <= in Excel.
Example
Suppose you consider the data for ALL 156 days they recorded the jams and you want to
know how many of those days there were more than 8 jams per day. You would type:
=COUNTIF(B2:B157,">8")
to get a result of 104.
Practice
Find the number of days within the first 30 days in which there were 10 or fewer jams.
Answer: 16
Practice
Find the number of days within the days 20 to 90 (inclusive, meaning you include days 20
and 90) in which there were more than 15 jams.
Answer: 18
Practice
Find the number of days within the entire set of days in which the machine jammed exactly
20 times.
Answer: 12
The COUNTIF command can also count cells in which specific text appears. For example, the
attendant on duty is recorded in the third column of the file Count.xls. We can ask how often any of
those people were on duty.
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Example
To find the number of times that Hector was the attendant during the first 60 days, we would
type:
=COUNTIF(C2:C61,"=Hector")
to get a result of 14.
Practice
Find the number of times that each of Jane, Bob, and Mary are the attendants from Day 1
through (and including) Day 100.
Answer: Jane = 28; Bob = 20; Mary = 29
The RAND command
Sometimes it is helpful to have Excel generate random numbers for you. To generate a random
number between 0 and 1, we use the RAND command.
Example
To generate a random number between 0 and 1 in a cell, simply type:
=RAND()
Note that you need the two parentheses after RAND with nothing in them. Weird, but
necessary.
This command will continually change the number in that cell every time you do a new
computation, enter data into a new cell, or press the F9 key. Try it....press F9 over and over and
you’ll see the number change.
If you need several random numbers in a column or row, simply copy right or copy down from a
cell that has the RAND command inside of it. This will generate as many random numbers as you
may need.
Sometimes, you don’t want the random numbers to constantly change. One way to fix their value is
to select all the cells you want to fix and then copy all of data using CRTL-C on the keyboard.
Then click on the first cell in the range (upper left corner if you’ve selected a block of cells) and
then right click. If you choose “Paste Special…” you will see the following box appear:
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You can also use the Paste button on the Ribbon to bring up the same box.
If you choose Values (in the box) or Paste Values (from the menu), then Excel will paste in the
current random values as fixed numbers. Note that when you do this, all your randomization in
those cells will go away for good.
The RANDBETWEEN command
While the RAND command returns numbers between 0 and 1, there are times when you want to
generate numbers outside that range. The RANDBETWEEN command will generate random
integers between any two integers that you specify. The syntax for the command is:
=RANDBETWEEN(bottom,top)
where bottom is the smallest possible integer you want returned and top is the largest.
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Example
Suppose you want to generate a random number between 1 and 100. Then you type:
=RANDBETWEEN(1,100)
to get a random number. Note that like the RAND command, cells with this command in
them will change with F9 or other entry into your spreadsheet.
The IF command
The IF command is one of the most useful tools you will encounter in Excel. It allows you to ask
questions about data and then, based on the answers to those questions, return results that are
desired. We will start with basic usage of the IF command and then expand it just a bit. The syntax
for the IF command is:
=IF(condition, yes result, no result)
where condition is the question you ask, yes result is the value, result, or cell that is returned if the
answer to the question/condition is yes, and no result is the value, result, or cell that is returned if
the answer to the question is no.
Let’s start with some simple examples.
Example
Let’s go back to our copy machine example. In the file JamsPart2.xls, a new column has
been added to indicate whether or not the number of daily jams is acceptable or not. The
new file looks like this:
In the “Acceptable?” column, we will use the IF command to indicate whether or not the
number of jams is acceptable. We will arbitrarily decide for this example that if the number
of jams is less than 8, then that is acceptable, otherwise it is not. If it is acceptable, we will
place a 1 in that row, if not then we will place a 0 in that row. Here is how you would issue
that command in cell D2:
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=IF(B2<8,1,0)
Once you have the formula entered into cell D2, you can use the Copy−Down command
(Ctrl−D) so that it applies to all the rows on the sheet. When you do so, you get the
following:
To save space, only the first few rows are shown.
Example
In the previous example, having 1’s and 0’s may not mean much to someone unfamiliar with
the sheet, so let’s put “Yes” or “No” in the Column D instead. When you want to return text
as a result rather than a number, then you put the text in quotes. Here’s how you would do it
in this example:
=IF(B2<8,"Yes","No")
This produces a very similar result:
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Example
There may be times when you want either of the Yes or No returns to be a blank cell with no
text or numbers. To do this, you enter two quotation marks next to each other (“”). For
example, let’s say we want a “Yes” to appear if the number of jams is below 8, but a blank
cell otherwise. The command would be:
=IF(B2<8,"Yes","")
This gives the following:
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Practice
In the acceptable column, use the IF() command to place the works “Oh Yeah” if the
number of jams is 10 or less and the words “No Way” otherwise:
Answer:
Example
Sometimes you want to return a cell value already in existence rather than a fixed value as in
the examples above. This is easy. Let’s say you have a tax system where anyone making
less than $35,000 per year pays 20% in taxes. Anyone making $35,000 or more pays 22% in
taxes. (The U.S. system is a little different, with a staggered tax system, but this is a simple
example.) What we want to do is calculate how much tax a person pays given their income
and we want to do it for many individuals. The file Taxes.xls has data that looks like this:
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In the “Total Taxes” column, we want to calculate how much tax each income would pay. In
this example, we need to test whether or not the income is above $35,000. If it is, then we
multiply that amount by 0.22. Otherwise, we multiply it by 0.20. Here is what the command
in Cell B2 would look like. Make sure it seems reasonable to you:
=IF(A2<35000,A2*0.2,A2*0.22)
This will return the following results:
Note that the values that are returned can include cell references and numbers, as well as any
computations that are needed.
Practice
Use the Taxes.xls file to fill in the “Total Taxes” column with the following tax structure. If
you make $27,500 or less, you pay 12% in taxes. If you make more than $27,500, you pay
15.5% in taxes. Make sure you use the IF command.
Answer:
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Practice Challenge
Use the Taxes.xls file to fill in the “Total Taxes” column with the following tax structure: If
you make $25,000 or less per year, you pay 15% on your income. If you make more than
$25,000 per year, then you pay 18.5% of all income over $25,000 plus 15% of the first
$25,000. Read that carefully. (This more like the U.S. tax system, where we have tax
“brackets.”)
Answer:
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The VLOOKUP command
In some situations, you may have a large amount of data in two or more columns and your task is to
look up values in one column and return a value from a different column (in the same row).
Example
The file CarSales.xls gives a list of 450 salespeople. Column A gives the salesperson’s ID
number and Column B gives their sales for the month. As a manager, you want to lookup
any salesperson by their ID number, type it into Cell D2, and have their sales total returned
in Cell E2.
The VLOOKUP command will do this, but you have to be careful with the syntax. The form
of the command is as follows:
VLOOKUP(lookup_value,table_array,col_index_num,range_lookup)
where lookup_value is the value you are looking up, table_array is the entire set of data
from in which you are looking up values and returning values, and col_index_num is the
column of data that gets returned once the lookup value has been located. We will not use
the range_lookup parameter.
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In our example, we want to look up the value in D2 somewhere in the table array that starts
with cell A1 and extends down to cell B451. Upon finding the correct number, it should
return the value in column 2 of the table array. So, our command would look like this:
=VLOOKUP(D2,A1:B451,2)
This gives the cell or value
that you want to first
lookup. VLOOKUP will
look for this value in the
array and then return
whatever is in the
corresponding column that
you specify later in the
command.
This gives the table array
where all the data exists.
You must make sure that
both the data you are
looking up and the data
you are going to return
are including in this
array.
The 2 indicates to
take whatever
value is in the
second column of
the table array.
Important Note: The data in the column that contains the values you are looking up must be
sorted so they are in order. If they are not, then VLOOKUP will not work correctly.
Practice
The file Grades.xls is a list of 100 students, their cumulative GPA’s, and their academic
status. A school counselor uses it to lookup GPA’s by student number. Modify this
spreadsheet so that Cell F2 returns the GPA for the Student ID number entered into Cell E2.
Practice
The file Grades.xls is a list of 100 students, their cumulative GPA’s, and their academic
status. A school counselor uses it to lookup GPA’s by student number. Further modify this
spreadsheet so that Cell G2 returns the academic Status for the Student ID number entered
into Cell E2.
Practice
The file Grades.xls is a list of 100 students, their cumulative GPA’s, and their academic
status. A school counselor uses it to lookup GPA’s by student number. Add the title
“Probation?” to in Cell H1. Use the IF command to put a “Yes” in Cell H2 if the person’s
GPA is below 2.0 and a “No” in Cell H2 if the GPA is 2.0 or greater.
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The HLOOKUP command
In some situations, you may have a large amount of data in two or more rows and your task is to
look up values in one row and return the value from a different row (in the same column). This
command is almost exactly the same as VLOOKUP except that your data is organized differently.
Example
The file Stocks.xls is a list of prices for a new, popular stock. The Day row gives the number
of days the stock has been selling on the NASDAQ. Part of the file looks like this:
Since there are over 200 prices, we don’t want to have to scroll to lookup a particular day’s
stock price. The HLOOKUP command will do this for us. As you can see below, it’s syntax
is almost identical to the VLOOKUP command.
=HLOOKUP(lookup_value,table_array,row_index_num,range_lookup)
To lookup a stock price in Stocks.xls, the command would be:
=HLOOKUP(B4,A1:IV2,2)
Make sure you open the file and understand how the command works. The command for the
screen shot above is shown below:
Practice
The file Population.xls gives estimates for the U.S. population from 1790 and forward, as
well as fabricated estimates for the percentage of the population that was female. Modify the
file using the HLOOKUP command so that when a year is entered in to Cell A5, the correct
and corresponding population and percents are returned in Cells A6 and A7.
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The INDEX command
There is one more command that can help you look up values in a list of data. It’s more limited that
HLOOKUP and VLOOKUP, but it can come in handy for some of our course projects.
Example
The file Index.xls has two columns of randomly-generated numbers. Open this file and
repeatedly change the value of Cell E2, which is labeled Input. Also, look at the formula in
Cell E3 to view the INDEX command. See if you can tell what is happening and then come
back and continue to read.
You’ll notice that if you put a 6 in cell E2, it returns a value of 28. Note that there are
several rows which have a 6 in the Random A column. The first one is Row 3, where 6 is
associated with 40. Row 20 also has a 6 in the Random A column with a 26 in the Random
B column. So the INDEX command does not do a lookup for the value of 6. Instead, it
simply looks up whatever is in the 6th row of the specified array (in this case A1:B24) and
returns whatever value is in Column 2 of the array. That’s why the command in E3 is:
=INDEX(A1:B24,E2,2)
This gives the
array in which
you look for
data.
This tells you the
number of the row to
look up.
This says to return whatever
value is in the second
column of the appropriate
row. If this had been a 1, it
would return the value in
the first column.
Note that if you type a 1 in Cell E2, Excel will return “Random B” in Cell E3. A picture of
this is given below.
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Practice
Modify the file Index.xls so that the Array in Cell E3 to be considered is only Cells A7 to
B20. (This is a smaller array that the previous example. Also, the first row of the new array,
which has the numbers 7 and 14 in it, will now become “Row 1” for the purposes of the
INDEX command.) Type in the number 5 into Cell E2. What number do you get?
Answer: You should get a 30, not a 28.
You may be wondering why you would use INDEX when you have VLOOKUP. Here is an
example similar to what you may see in a class project where INDEX might be helpful.
Example
The file CarIndex.xls is a list of the number of cars sold per day at a dealership during a oneyear period. What we often need to do is randomly pick one of those days and then see how
many cars were sold on that day. It’s like having 365 slips of paper (one for each day) and
the number of cars sold on a day written on the papers. We put them into a big shoe box and
then randomly pick one out, recording the number of cars sold. This is often called sampling
and will play an important role in MATH&148. When you have hundreds, or even
thousands, of records to choose from, Excel’s INDEX command will allow you to do this.
Look at the file:
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In Cell E2, you can check to see that a random number between 1 and 365 has been
generated. Do that now. Now, look at the contents of Cell E3. In this cell, the INDEX
command has been used to select both columns A and B, Cell E3 is specified to contain the
row number we are to look up, and the second column (Column B) is the data to be returned
by Excel. If you press F9 repeatedly, you’ll see the equivalent of a new slip of paper being
picked out of a shoe box (after the previous slip has been replaced).
Now, look at Sheet 2 of CarIndex.xls which has the same data as Sheet 1 does. Hit F9 a few
times and you’ll notice it behaves just like Sheet 1 does. However, notice that the Random
Number cell has been deleted. Look at the contents of Cell E3. You will notice that we have
built the generation of the random number directly into the INDEX command:
=INDEX(A3:B367,RANDBETWEEN(1,365),2)
Instead of specifying a specific numerical value or
cell reference as before, I’ve told Excel to generate
a random number between 1 and 365 and to use that
as the number of the row to look up. The second
column still remains the one that gets returned.
A picture of the formula bar is given below:
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Practice
The file PhoneLog.xls gives a list of 750 phone calls tracked by a telemarketing company.
The call number is logged along with the amount of sale made on that call. In Cell D2, use
both the INDEX command and the RANDBETWEEN command to randomly pick one of
the calls on the list and return the sale amount for that call.
Optional: How I Built the Phone Log File
Here’s how I built the PhoneLog.xls file for this example. You may find it interesting as it uses
many of the commands in this section.
First, I entered 54869 (an arbitrary number) into Cell A2.
In Cell A3 I entered =A2+1 so that it would increment the number for me.
I then copied Cell A3’s formula down so that 750 data points were generated.
In Cell B2 I entered the following: =IF(RAND()>0.7,RANDBETWEEN(15,300),0)
What this did was use RAND() to generate a number between 0 and 1. If that number was
greater than 0.7, then I used RANDBETWEEN() to generate a sales amount between $15
and $300. If the initial random number was less than or equal to 0.7, then I recorded a sales
value of $0. My thought process was that 70% of the phone calls would lead to no sales,
while 30% would lead to sales.
I then copied Cell B2’s formula down so that 750 sales data points were generated.
I selected all the cells in columns A and B that had numbers in them (1500 in all) and copied them
with CTRL-C.
I then clicked on Cell A2 and did a Paste Special...→Values command so that all the ugly formulas
were gone and only the numerical values remained.
This is how many of the files in this tutorial were generated. Very easy.
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Graphing
Basic Graphing
Graphing a large amount of data by hand is tedious and very prone to error. Excel will graph data
quickly and easily.
Example
Fuller and coworkers (1997) estimated the Costs of a medium-sized cotton gin plant as shown
in the file Cotton.xls. Open this file to view the data. To graph this data, we will use the Chart
Wizard. Here are the steps you take to graph this data. Please do them as they are described
below to make sure you get some practice.
Select the data: Use your mouse to drag and select all the data to be graphed. Include the
heading row.
Start the Chart Wizard: Click on the Insert tab on the Ribbon:
Select the Chart Type: As you can see, you have many choices of graphs to choose from. In
this course, we will mainly use Column, Line, and Scatter graphs. For this example, let’s
choose the Scatter choice. We’ll use the first choice in the list, as shown below:
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That will generate a graph that looks like this:
This is your first glimpse at what the data looks like. We can refine our picture.
Refine your Graph: There is, unfortunately, no uniform way to change all elements of the
graph. However, RIGHT CLICK often is a good first step. Let’s do some examples so you
can see what I mean.
Change the Title: Click on the “Thousands of $” text until it is boxed, like below:
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If you RIGHT CLICK with the mouse inside the box, you’ll get a menu:
Although it does not appear above, there is often also a menu for changing the font style, size,
color, etc. You can use this to change the title as you see fit. You can select “Edit Text” to be
able to change the text as well. I’ll change some things around so it looks like this. Follow
along and make the same changes to insure you know how to alter the graph.
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Change the Graph’s Point Style: We can change the color/style of the points as well. LEFT
click on one of the points. Then make sure the Ribbon is set to show the Design tab. It should
look like this:
You can see boxes at the top that allow you to change the colors of the points. Also, you can
see many more options by clicking on the drop-down arrow in the lower right corner,
highlighted below:
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This will bring up many options, only a few of which are shown below:
It’s easy to select one and change the look of the graph. We’ll go to read with shadows:
Change the Axes: We can also change the way the axes look. For example, RIGHT click on
the vertical axis and then choose “Format Axis…” from the list.
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You’ll get a box like this:
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There are numerous options and changes you can make, as you can see. One common change
is to alter the Number settings. Select “Number” from the list on the left:
You can choose general numbers, currency, dates, etc. I’ve chosen the second option,
“Number” which allows me to specify how many decimal places to show. Choosing 2 and
then clicking the “Close” button produces a graph with a vertical axis showing two decimal
places, as below:
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Adding Labels to Axes: Sometimes, you will want to add descriptive labels to your axes. To
do this, first LEFT click the graph and then choose “Layout” from the Ribbon.
This give you many new options, including Chart Titles, Axis Titles, Data Labels, etc. You
can experiment with these options on your own. Here, we’ll just add an Axis Title to the
horizontal axis. Choose “Axis Titles” button and then “Primary Horizontal Axis Title,”
followed by “Title Below Axis.” It looks like this:
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When you select this option, the graph will add an axis title.
You can edit this by clicking inside the box and changing the text.
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You can also do this for the other axis as well.
Changing the Chart Type: The next big thing to change is the Chart Type. Let’s first suppose
we want to add lines to connect the red dots. LEFT click on the graph and then choose the
“Design” tab from the Ribbon.
Now choose the “Change Chart Type” button on the left:
A window will appear that looks like this:
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All the different chart types are listed, so it’s easy to make a change. You can experiment and
see how this data would look using different displays. For now, we’ll choose the second
option on the XY (Scatter) list:
When we do so, the graph changes to the following:
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If the line is too think, we can RIGHT click on the line (not a point) and then choose “Format
Data Series…” and then go to the “Line Style” section. Changing the “Width” to 2 produces a
nicer look.
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Following this same basic procedure, we can view this data as a bar chart. I’ve changed the
chart type and the bar colors to blue in the picture below. Can you reproduce the picture?
Using these tips and tricks, you can make the graph look any way you want. Keep in mind that
the way your reports look is often very important out in the business world. Therefore, you
should strive to have professional-looking graphs in MATH116 and MATH&148.
Practice
In the file Retire.xls you will find a list of annual interest rates and dollar values. The “First
Year Income” is the amount this particular retiree can expect to receive in her first year of
retirement, given different rates of return on her investments while she works. For example, if
she earns an average of 6% annual interest on her retirement investments, when she retires her
first year of retirement income benefits will be $98,856. Use this data to create a line graph
that looks like the one below. NOTE: If you are using a black and white printed copy of this
tutorial, you will not be able to see the colors that are specified so please open the electronic
version of the tutorial to see this level of detail. Note that many of the font sizes, colors, and/or
styles have changed. You don’t have to get it exactly like you see below...what’s important is
that you know how to change each of the components of the graph. Remember, if you want to
edit a piece of a graph, start by trying a RIGHT click on that object. Also, selecting different
tabs in the Ribbon is also usually useful. It takes some time and practice, but it gets easier if
you do so.
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Sherice's Retirement Money
$300,000
Income
$250,000
$200,000
$150,000
$100,000
$50,000
$0%
2%
4%
6%
8%
10%
12%
14%
Rate of Return
Note on Bar Graphs
The easiest way to create bar graphs is to start with an XY (Scatter) plot and then to change
the Chart Type to a Bar graph. If you start with choosing a Bar graph, you can get some nonintuitive results that require some fiddling with the chart’s settings. Try it...you’ll probably
find I’m correct on this one. When we get to Histograms, we’ll need to deal with this matter
much more carefully, so for now, if you want a basic bar graph, start with an XY (Scatter)
graph.
Graphing Functions
You are undoubtedly familiar with functions from previous math courses. For example, the function
f ( x) = x 2 has a graph of a parabola that opens upwards from the origin. We want to explore how to
graph this, and any other function, using Excel. There are two main steps: (1) Identify how much of
the graph you want to see left to right (the domain), and how many subintervals/points you want to
graph so you can create a list of data points in Excel and (2) Use the Chart Wizard to graph the
function.
Example
Let’s graph f ( x) = x 2 from -10 to +10 on the x axis and include 25 subintervals total in our
graph.
Part (1)
We’ll say that the interval we are graphing is [-10,10], which has the general form [a,b]. In
these examples and the spreadsheets we will use, a is the leftmost endpoint to be graphed and
b is the rightmost.
If we take the value b-a, we get the total length of the domain. In this case
a − b = 10 − ( −10) = 20 . So our interval is 20 units long (-10 to 0 and then 0 to 10).
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Our next step is to take that entire interval and compute the length of each subinterval. The
length of this space will be called the subinterval length and we will use the symbol Δx to
represent it. We simply need to take the length of the interval and divide by how many
subintervals we have to get Δx . In this case, we have:
10 − (−10) 20
Δx =
=
= 0.8
25
25
(Technically, if we have 25 subintervals we need 26 points. You always need one more point
than you have subintervals {why?}. When graphing functions, we will divide by the number of
subintervals, which is always one less than the number of points needed.)
The top of the file Parabola.xls shows how these have been entered and computed in Excel.
You should open this file and examine the formulas and entries in cells B1 through B5 before
continuing. A snapshot is show below:
The following picture shows which formulas were used in each cell. (You can use CTRL-` to
toggle between Data view and Formula view...it’s a handy feature to know about.)
Part (2)
In this next part we need to generate a list of (x, y ) points to graph. We start with the left
endpoint (a) which is -10 in this example. That’s our first x value. The next x value is the
previous one PLUS the length of each subinterval. In this example, it would be −10 + 0.8 =
−9.2. The third x value will be −9.2 + 0.8 = −8.4 and so on. We certainly don’t want to
compute and type these in by hand so we will have Excel do it.
In Cell B8, the value of a is entered. In Cell B9, we need to take Cell B8 and add Δx = 0.8 to
it. We could enter into Cell B9 the formula =B8+B5. However, when we copy this down,
Excel will assume we want relative references and it will change B5 to B6, which is blank.
This is an example of when we need to utilize absolute references to get the results we desire.
So what we put into Cell B9 is =B8+$B$5. Recall that the dollar signs lock us into using
Column B and Row 5. We can then copy this down to get to +10 for the last x value. Open the
file Parabola.xls and see how this was done. Make sure you understand how the x values have
been generated and note that there are exactly 26 points (25+1), as discussed before.
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We can now easily generate the y values. In Cell C8, the simply formula =B8^2 is entered to
take the x value in Cell B8 and square it. Don’t forget, the function is f ( x) = x 2 , so this
makes sense. We now use Ctrl−D to Copy Down our formula and then insert a Scatter graph
with no connection lines…just the points. This gives the following graph, making no other
special changes:
Of course, we could pretty this up, but the main thing we note here is that we usually don’t
graph functions with dots. We usually prefer nice smooth curves or lines without the dots.
Let’s change the chart type to a smooth line graph with no data points. The choice is
highlighted below:
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This gives us the following graph, which we can pretty up with colors, labels, etc. as we see
fit. See the sheet “Chart2” of the Parabola.xls file for a nice picture of the parabola.
Practice
See if you can duplicate the look and feel of the parabola that is shown in the Chart1 sheet in
Parabola.xls.
Example
Let’s graph another function, g ( x) = x − 5 ln x + x 3 . We will use the interval [5,30] and plot
50 subintervals. Rather than go through each step like above, it might be better to simply
open the file G(x).xls and see what it looks like. The only thing that has changed is that the
function formula is different in Column C, and the interval information is different. This is
what the final graph looks like this:
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Please make sure you explore and understand this file before trying the practice problems
below.
Practice
Graph f ( x) = 2 x 3 − 5 x + 3 on the interval [−5,8] using 75 subintervals. See if you can graph
this without using or looking at the files Parabola.xls or G(x).xls. If you get stuck, use those to
guide you. The goal is to graph this function from scratch.
Answer: Your graph should look like this:
Graph
1200
1000
800
600
400
200
0
-10
-5
0
5
10
-200
-400
Practice Challenge
2
1
Graph f ( x) =
e − 0.5 x on the interval [-5,5] using 100 subintervals. This is a key
2π
function in MATH&148 that you will see a lot of when you get there! See if you can graph
this without using or looking at the files Parabola.xls or G(x).xls. If you get stuck, use those to
guide you. The goal is to graph this function from scratch.
Answer: Your graph should look like this:
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Graph
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
-5
0
5
Graphing Histograms
Our last goal in this section is to master the method of graphing histograms. These are important in
MATH116 and MATH&148 and it’s important you can create these without a lot of fuss (after
some practice, of course). Histograms are tools used to depict data and to see how the data is “piled
up.” For example, here is a histogram that shows how prices of stocks in the S&P500 are
distributed. (The data is completely fabricated!).
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Stock Distribution
Each of these
bars
corresponds to
a bin on the x
axis.
120
Number of Stocks
100
80
60
40
20
These
values are
0
the
midpoints
of the bins.
-
$3.35
$9.85
$16.35
$22.85
$29.35
$35.85
$42.35
$48.85
$55.35
$61.85
Price
This histogram has information about 500 stocks in it. It is therefore an efficient way to present the
data. For example, we see that about 110 stocks have prices that are centered around $22.85.
There are 10 bars on the graph, each of which corresponds to what is called a bin. A bin is simply a
range of numbers into which a stock price could fall. For example, if a stock price falls between
$6.60 and $13.10 (called the bin limits), whose midpoint is $9.85, then it gets placed into the
second bin from the left. As more stocks fall into that bin, it rises in height. The more stocks in the
bin, the higher the vertical bar. We will discuss how to compute the bin limits, number of bins to
use, and the bin midpoints as we progress, but what’s important now is that you have a basic
understanding of what the histogram tells you: it counts up values, assigns them to pre−determined
bins, and then displays the results with vertical bars.
Note: You MAY need have the Analysis ToolPak and the Analysis ToolPak VBA Add−Ins installed
to use this feature! To do so, click on the large Office logo in the upper right of the Excel window:
Then choose “Excel Options” at the bottom of the menu that appears. You’ll get a screen that looks
like this:
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Click the “Add-Ins” from the list on the left and then the “Go…” button near the bottom of the
screen. This will bring up a list of Add-Ins you can install. (You may need your Office disk to do so.)
We suggest you add the Analysis TookPak, Analysis ToolPak-VBA, and the Solver Add-In modules.
BACK TO HISTOGRAMS:
The major steps to graphing a histogram are as follows:
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Step 0: Get the data in a spreadsheet if it’s not already there
Step 1: Determine the Minimum, Maximum, and Range of your data to determine the bin limits, bin
widths, and midpoints.
Step 2: Use the FREQUENCY command to count how many data points are in each bin.
Step 3: Insert and format a vertical column chart to create the histogram.
Let’s dissect these steps one at a time using the Stock Data shown above. Open up the file
SP500.xls and follow the steps below carefully. Do one at a time. Do not move to the next step until
you understand the current one.
Step 0:
Open the file SP500.xls. The data is already entered for you.
Bins and Midpoints
Step 1:
(As you move through these steps, you can check the “Results” Sheet to see what is being
discussed.)
Let’s first count how many data points we have. In Cell C3, type “Data Points” and use the COUNT
command in Cell D3. (You should get 500.)
Label Cell C4 as “Min” and use the MIN command in Cell D4 to find the minimum stock price.
(You should get 0.15)
Label Cell C5 as “Max” and use the MAX command in Cell D5 to find the maximum stock price.
(You should get 64.13)
Label Cell C6 as “Raw Range” and compute the Range of data in Cell D6. (You should get 63.98)
Label Cell C7 as “Subintervals.” We need to determine how many bins (i.e. subintervals) to use. If
we use too few or too many, we get very inaccurate and useless histograms. Therefore, the number
of bins, and hence the bin width, is important to pay attention to. (See this link for an interactive
demonstration on how bin width can affect the look of the histogram.) In this course we will use
the following formula to estimate the number of bins to use. We let N be the number of bins and n
be the number of data points in the set:
N = 1 + 3.3 log(n)
In this file, we have n = 500 so the formula give us:
N = 1 + 3.3 log(500) ≈ 9.9
In general, let’s agree to Round Up to the next integer to get the number of bins. (We can’t have 9.9
bins, right?) Hence, we have 10 bins.
When we graphed functions we determined our interval, [a,b]. We’ll do the same here. We could
take the min and max to be the endpoints of the interval, but if they are not nice numbers, it’s
sometimes better to round them a bit. In general, round down to the nearest integer for the left
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endpoint and round up to the nearest integer for the right endpoint to make sure all your data points
are in your final interval.
Label Cell C8 as “a” and Cell C9 as “b.” Use the ROUNDUP and ROUNDDOWN commands to
compute these. (You should get a = 0 and b = 65. )
Label Cell C10 as “Bin Range” and compute the range for the interval [a,b]. (You should get 65.)
Label Cell C11 as “Delta X” and compute this value by dividing the range by the number of bins.
(You should get 6.5)
At this point, the spreadsheet should look something like this:
The formulas in column do look like this:
Now you can create a list of bin limits, starting with a = 0 and ending with b = 65 by adding Delta x
to the previous bin limit. See the list starting in Cell D15 of the sheet “Results” if you are not sure
what is meant. This is very similar to what we did when we generated the list of x values when we
were graphing functions. Before you go on, makes sure you create your own bin limit list on the
Data sheet. It should be created in Cells D14 to D25, as shown in the “Results” sheet.
The bin limits you just created are the upper limit of the bin. That is, when Excel goes to assign a
value to a bin, it checks to see if it is less or equal to that bin limit value (but larger than the next
lowest bin limit). If so, it assigns that data point into that bin. Hence, if the bin limit is 13, then a
stock price of $13 will be assigned to that bin, not the one above it.
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The last step is to find the midpoint of each bin. This is not hard. The midpoint of each bin is simply
the computed bin limit minus one half of Delta x.
Bin Midpoint
Δx
Half of Δx
Bin Limit
Label Cell E14 as Midpoints and then compute the midpoints of each bin. For example, the first
midpoint in Cell E15 would be computed with =D15−0.5*$D$11. Note the $ sign is needed for an
absolute reference so we always subtract the value of Delta x. We can copy this down to get the rest
of the midpoints. Note that the first midpoint will be −3.5 which makes no sense in this context.
Hence, we will simply replace it with a dash (“−”) instead.
Here is what our sheet looks like up to now:
The formulas for these latest computations are shown below:
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Frequency Command
Step 2:
Once all of Step 1 is done, we are done with the hard part. Now we can use the FREQUENCY
command. This command computes how frequently data fall into particular bins. The general
format for this command is:
=FREQUENCY(data_array,bins_array)
As you can imagine, the data_array is the range of cells that holds your data, and the bins_array is
the range of cells where you have your bin limits. The FREQUENCY command has the great
advantage that if you change you data in your data array, the frequency counts will automatically
update. Hence, your counts are always up to date and if you have a histogram that is based on those
counts, the graph will also stay up to date.
Because we are going to fill in several cells at once, we select all the cells where we want frequency
counts to go. They are highlighted below:
We now enter the command by beginning to type the following command into cell F16:
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Note: We are NOT using the Midpoints yet!
IMPORTANT!!! Since we are wanting Excel to do computation for SEVERAL cells at once, we
cannot just hit the Enter key as normal. That would only compute the frequency for the first cell.
Instead, we use SHIFT-CTRL-ENTER. That is, hold down both the SHIFT and CTRL keys down
and then hit the ENTER key on your keyboard. If you do it correctly, you’ll get the following:
If you did not hold down the proper keys correctly, you may not get all the counts to show up. So
make sure you have this before you move on.
Formatting the Histogram
Step 3:
We now create a basic Column graph from the data in cell range F16:F25. First we select that data
range:
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Next, insert a 2-D column chart:
This gives the following crude graph:
First, let’s give it a title. Click on the graph and choose the “Layout” tab in the Ribbon. Then choose
the “Chart Title” button and the “Above Chart” option:
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Then edit the title to “SP500” to produce this graph:
The vertical axis gives the bin counts, as we want. But notice that the horizontal axis is labeled 1 to
10 (for the 10 bins). We want to replace those numbers with the mid-points of each bin, which are
located in Column E. To do this, RIGHT click on one of the vertical bars until a menu appears like
this:
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We want to choose the “Select Data…” option from the list to get this window:
Notice that on the right, there is a place to edit the “Horizontal (Category) Axis Labels.”
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So click on the “Edit” button and you’ll get a window that allows you to specify which labels to
use:
Our midpoint labels are in cells E16:E25 so use your mouse to highlight that range of cells:
That should produce the following graph:
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Since most histograms have little space between the vertical bars, we fix that next. Once again,
RIGHT click on one of the data bars and now choose the “Format Data Series…” option:
This will produce a window that allows you to change the “Gap Width” of the chart:
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Depending on your preferences (or your instructor’s preferences), you will typically want a gap
width between 0 and 5%. We’ll choose 5% here so that the bars can be distinguished from each
other but that the space between them is very small. Here’s the result:
Finally, the “Series 1” label on the right serves no useful purpose for this graph. So RIGHT click on
it and then choose “Delete” from the menu. Our final graph looks like this, and you should have the
same thing on your screen:
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Example
The file Disney.xls has a list of volume for Disney stocks on several trading days. In the sheet
called “Data and Student Workspace,” create a histogram with the data that looks very similar
to the following graph. Your x−axis labels may be slightly different. Check the sheet called
“Completed Histogram” to see how I got the graph.
Disney Stock Volume
20
Days
15
10
5
0
2800
6800
10800
14800
18800
22700
26700
30700
Shares Traded
Example
The file Basketball.xls has a list of heights (in feet) for professional basketball players. Open
the file and create a histogram of this data.
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Example
The file GPA.xls has a list of cumulative GPA’s for SCCC students. Open the file and create a
histogram of this data.
Trendlines
Trendlines are basically formulas that have been extracted from a set of data. While the issue is a bit
more complicated than that, we don’t need to get into the details too much in this tutorial. We use
Trendlines when we have a series of data in (x, y ) format and we want to find the equation of a
line, quadratic, or some other function that fits the data relatively well.
The first step to creating a trendline is to graph the points using (XY) scatterplots. After that, we run
the trendline routine.
Example
The file Shrinkage.xls has data about the amount of weekly merchandise lost to shoplifting
and damage (called shrinkage) as it relates to the average number of clerks on duty. A sample
of 7 weeks worth of data is shown.
Managers want to see if there is a relationship between these two variables and if so, they
want to predict shrinkage from the number of clerks on duty.
First, let’s graph this data using a simple (XY) scatter plot without any lines connecting the
data points. As a review, you may want to open the file and make sure you can get a graph
like this:
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Next, RIGHT click on one of the blue data points until the menu appears:
We will choose the “Add Trendline…” option. You should see this screen:
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This is where your intermediate and college algebra background will come in handy. You’ll
see a list of possible functions that could model this data. In this case, our data looks very
linear so we’ll keep the default choice of “Linear.”
Do no click the Close button yet!
We want to display the linear equation that best fits this data, so check the “Display Equation
on chart” box:
This should generate the following graph when you click the Close button:
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You will notice that a straight line has been drawn on the graph that corresponds to the linear
formula y = −3.0328 x + 52.508 . This equation is called the “line of best fit” because it is the
line that best fits this data. (No other line comes closer to fitting all of these points.)
Now, the equation that shows displays only a certain number of decimal places. If you want
more (or less) you can edit that as well. To do so, RIGHT click on the trendline equation and
choose “Format Trendline Label…” from the menu:
On the window that appears, choose the “Number” option from the Category list and then type
in how many decimal places you want displayed. We’ll do 10 for this example:
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This gives you the equation with many more decimal places showing:
IMPORTANT NOTE: The default number of decimals that show in a trendline (usually three)
are NOT necessarily rounded for you. To make sure that you have the level of accuracy you
desire, you should absolutely tell Excel to display several decimal places (as we just
demonstrated) and then round appropriately!!!
The LINEST Command
Sometimes, you may want the actual numbers that appear in the trendline equation to be
deposited into a cell so you can compute with them. To do this, we use the LINEST command,
which has the formt:
LINEST(known_y’s, [known_x’s],[const],[stat])
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For now, only the known-y’s and known_x’s are useful for us. They are, of course, just the y
and x values, respectfully, used to create the graph. To use this command, you highlight TWO
empty cells…one for the slope of the line and one for the y-intercept. We’ll do this in cells E2
and F2.
Like the FREQUENCY command, we start typing the command directly but don’t use the
ENTER key right away. The command looks like this for this example:
Since we want Excel to compute for more than one cell, we have to once again use SHIFTCTRL-ENTER. When we do this we get the following:
We can now increase the size of these cells and tell Excel to show more decimal places.
More importantly, we can compute with these numbers without losing any accuracy through
rounding.
Practice
Use the file TotalCosts.xls to find the line of best fit trendline for the data given.
Answer:
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Practice
Use the file Demand.xls to find the line of best fit trendline for the data given.
Answer:
Linear trendlines are not the only kind we can generate. We can also do quadratics (Excel calls
these polynomials of Order 2), log graphs, and exponential graphs. In MATH&148, we’ll see how
these are useful.
Example
Open the file Shoes.xls to see data about how much it cost to produce shoes in 1937 (actual
data!). While the data looks linear, we may also suspect that it is quadratic. We can produce a
scatter plot, as usual, and then Start our Trendline tool:
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Note that we have selected “Polynomial” with “Order” 2. This is a quadratic of the
form y = ax 2 + bx + c . The order of a polynomial tells you the highest power you find in the
function. When we select this and use the Options tab to specify the equation, we get the
following graph:
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You can see that this is not a straight line but is actually a small piece of a parabola. The
equation shown is also (obviously) not linear as well.
In this way, you can take data points and fit them with different function models. Some
models are better fits than others, but your coursework will have more to say about that.
Well, that’s the end of the tutorial. Please keep a copy of this
around so that you can refer to it during MATH116 and
MAH&148. We’ve covered a lot of ground so we’re all bound
to forget some of the details we’ve encountered. Good luck
with your projects.
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