Using Spreadsheets to Solve Problems
1.9 - REFERENCE FUNCTIONS
In a previous chapter it was shown how IF functions can be nested to decide between a set of
possible outcomes. IF functions, however, are limited to seven levels of nesting, allowing for at
most eight different outcomes. Furthermore, it quickly becomes apparent after two or three
levels of nesting this method can be cumbersome and time consuming to implement.
Excel provides another category of functions designed to look up values from a given list
and return a corresponding value. In this section, we will use one of the simplest Reference
functions, the LOOKUP function.
THE LOOKUP FUNCTION
THE LOOKUP FUNCTION SYNTAX
The LOOKUP function is a function designed to look up values from a given list and return a
corresponding value. The LOOKUP function takes a specified criterion (either a label or a value)
and searches for a matching entry in a one-column or one-row range. When a match is found, it
returns the cell contents (either a value or label) from the same position of a corresponding onecolumn or one-row range. The LOOKUP function has two syntax forms: vector and array. This
chapter will discuss with the vector form of the LOOKUP function:
LOOKUP(lookup_value,lookup_vector,result_vector)
The arguments of the vector form of the LOOKUP Function syntax are as follows:
Lookup_value is a value that the LOOKUP function searches for in the first vector. This value
can be a number, text, logical value, or a name or reference that refers to a value. It can be
thought of as the criteria you wish to match.
Lookup_vector is a range of cells used to search for the lookup_value. This range must be
one dimensional, containing either cells in a single row or a single column. The values in
lookup_vector must be placed in ascending order.
Result_vector is a range of cells that contain the values you wish to return. It too contains
either one row or one column, and must also be the same size as lookup_vector.
The results of a LOOKUP function can be one of the following:

If the value you are looking for exactly matches a value in the lookup_vector then it will
return the corresponding entry on the result_vector.

If the lookup_value does not match an entry in the lookup_vector exactly, it is matched
to the largest value in lookup_vector that is less than or equal to the lookup_value.

If the lookup_value is smaller than the smallest value in lookup_vector, LOOKUP
returns the #N/A error value.
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To illustrate how the LOOKUP function works, consider the following
formula based on the worksheet in Figure 1:
=LOOKUP(“Jane”, A2:A5, B2:B5).
A
B
1
Name Age
2
Alice
15
3
Jane
17
4
Mike
9
This formula will match Jane to the entries in the column range A2:A5. It 5 Sam 22
will return the corresponding value in the column range C2:C5. If Jane does
Figure 1
not appear it will find the “closest” match alphabetically. In this case the
formula finds Jane in the second row of the lookup_vector range, so it will
return the second value in the result_vector range, which corresponds to the value 17.
THE LOOKUP FUNCTION USING A HORIZONTAL ORIENTATION
Here is an example of a lookup table in a horizontal format. In Figure 2 cells A1:E2 contain a tax
schedule. Taxes are calculated on a progressive scale: incomes under $25,000 have no tax (0%),
incomes of at least $25,000 but less than $50,000 are taxed at 10% of income, incomes of at
least $50,000 but less than $100,000 are taxed at 15% of income, and incomes of $100,00 or
more are taxed at the rate of 23%. In cell A5:C10 is a list of employees and their taxable income.
In cell C6, write a formula to determine the income tax for the employee Jonas, such that it can
be copied down the column.
A
1
2
3
4
5
6
7
8
9
10
Income:
Rate:
Employee:
Jonas
Maria
Zev
Marta
Alex
B
$
$
$
$
$
$
C
Income Tax Rates:
$
25,000 $
0%
10%
Income
73,250
27,350
1,094
92,125
48,999
$
$
$
$
$
D
50,000 $
15%
E
100,000
23%
Tax Due
10,987.50
2,735.00
13,818.75
4,899.90
Figure 2
For just Jonas the solution =B6*D3 can be used – Jonas’s income multiplied by the
corresponding tax rate. However this approach will not work when the formula is copied down
the column: income varies relatively (B6) but the tax rate (D3) neither stays the same nor
changes relatively, as it is dependent on the income value. Another way to approach this would
be to use a nested IF function:
= B6*IF(B6<C2, B3, IF(B6<D2,C3,IF(B6<E2, D3, E3)))
While this function works, it’s somewhat tedious to write and if more tax levels are added, the
formula is difficult to maintain. Furthermore, if there are more than 8 different tax levels, this
approach will no longer work. A more efficient method of solving this problem is to use a
LOOKUP function:
=B6*LOOKUP(B6,B$2:E$2,B$3:E$3)
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This formula will multiply the value $73,250, the income in cell B6, by corresponding tax rate.
To find the corresponding tax rate the LOOKUP function will match the value in cell B6, the first
argument of the function, to the values in the range B2:E2, as specified in the second argument
of the function. Once a match is found, the corresponding value in the result vector (the third
argument specified as B3:E3) will be returned.
Note several features of this formula:




The lookup value is a cell reference. This reference will copy relatively to match each
successive employee’s income.
The lookup and result vectors contain absolute row references so that when the formula is
copied down these ranges will not be affected.
The values found are NOT exact matches. i.e., $73,250 does not appear in the lookup vector
range B2:E2. Rather the greatest value in the lookup vector range that does not
exceed the lookup value is selected and the corresponding value in the result vector is
returned.
Both the lookup_vector and result_vector ranges do not include titles. These ranges
start with the first value and end with the last value – no additional cells should be included
in the range.
How is the corresponding value found? The exact algorithm (step-by-step method) is not
specified but one possible logical method might be as follows:




The first category $0 is less than the lookup value $73,250 so the next value is considered.
The second category $25,000 is again less than the lookup value $73,250 so again the next
value is considered.
The third category $50,000 is less than the lookup value $73,250 so the next value is
considered.
The fourth category $100,000 is more than the lookup value $73,250 so the previous value
is matched – that of $50,000. $50,000 is the third value of the lookup vector, so the third
value of the result vector, 15% in cell D3, is returned.
Again this is not the “exact” method necessarily programmed into Excel. What is known is that
the user must list the lookup values in ascending order or the function is not
guaranteed to return the correct result.
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Using Spreadsheets to Solve Problems
A MORE COMPLEX EXAMPLE:
A
B
C
1
Price List:
2 Shipping $/lb.
$
0.50
3
4 Item No. $/each
Weight (lbs)
5
124 $
332
19
6
125 $
55
5
7
126 $
224
14
8
127 $
483
16
9
128 $
41
2
10
129 $
83
20
11
130 $
9
14
12
131 $
268
2
13
132 $
139
17
14
133 $
52
11
15
134 $
474
18
16
135 $
294
20
17
136 $
411
3
A
1
2
3
4
5
6
7
B
C
Customer Orders
Customer Item#
Qty
Zael
134
3
Orwich
127
4
Wagma
104
2
PT
134
10
PT
128
1
D
Total Price
$ 1,449.00
$ 1,964.00
#N/A
$ 4,830.00
$
42.00
Orders!
Figure 3
Pricing!
A more complex example is given in Figure 3. This workbook example contains two worksheets:
Sheet Pricing! contains a list of items numbers for various items you have for sale on E-Bay,
their corresponding cost per unit, and weight in pounds (lbs) per unit. Also given on this
worksheet is the shipping cost per pound. Worksheet Orders! contains a list of recent orders,
including the item number being ordered and quantity. To complete the Orders! worksheet
column D requires a formula to total the cost of this customer’s order, including the cost of all
items and shipping.

Step 1 - Understand the Problem.
Mathematically the customer’s order total is Quantity * (Price/Item + Shipping Cost/Item).
Since just the shipping weight in pounds (lbs) and cost per pound ($/lb) are given, this formula
can be further expanded to the following:
Quantity * (Price/Item + Weight/Item * $/lb to ship)

Step 2 – Translate to Excel Syntax.
If this formula is written directly, just substituting the appropriate values for Zael’s order, then
the cost per unit and weight would not necessary copy down correctly. Both of these values are
variable, but change by item number and not by relative position. Thus a LOOKUP will be
required. Can a single LOOKUP function return both the cost per item and shipping weight?
No, the LOOKUP function can return only one value at a time. So each variable, price/item, and
weight/item, will require a separate LOOKUP.
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Using Spreadsheets to Solve Problems
In pseudo code this formula will be: Quantity * (Lookup(item number, range of item numbers,
range of prices) + Lookup(item number, range of item numbers, range of weights) * $/lb to
ship). The cell references are as follows:
o The quantity is on the same worksheet as the formula (Orders!) in cell C3.
o The item number to be looked up is on the same worksheet as the formula in cell B3.
o The range containing the item numbers to lookup is on sheet Pricing! in cells A5 through
A17.
o The range containing the corresponding prices is on sheet Pricing! in cells B5 through B17.
o The range containing the corresponding weight is on sheet Pricing! in cells B5 through
B17.
o The cost per pound to ship is on sheet Pricing in cell C2.
Applying these cell references the formula is:
=C3*(LOOKUP(B3,Pricing!A5:A17,Pricing!B5:B17)+LOOKUP(B3,Pricing!A5:A17,
Pricing!C5:C17)*Pricing!C2)

Step 3 – Copying.
In addition to knowing that a LOOKUP function is needed so that the formula can be copied,
some of the arguments of the LOOKUP and the other operands must be considered. The
Quantity and Item Number will change relatively as the formula is copied down the column so
thus C3 and B3 are relative references. However, the lookup_vector and result vector ranges do
not change when copied and therefore must contain an absolute row reference. Lastly, the $/lb
for shipping in cell Pricing!C2 needs to be considered. Again this value does not change when
the formula is copied and thus requires an absolute row reference. The final formula will be:
=C3*(LOOKUP(B3,Pricing!A$5:A$17,Pricing!B$5:B$17)+
LOOKUP(B3,Pricing!A$5:A$17,Pricing!C$5:C$17)*Pricing!C$2)
One point worth noting is the value that results in cell Orders!D5 is #N/A. This is an error
message indicating that there is no corresponding answer. The reason for this is the
lookup_value 104 is below the smallest value on the lookup_vector list (124). This error can be
corrected either by changing the item number on the order to an existing item number from the
list, or by adding item 104 to the top of the price list. A more serious error would be using an
item number that is between the values in the lookup range or greater than those values. For
example if the value 138 is used as an item number, Excel will return the greatest value on the
list that does not exceed 138. Hence the pricing information for item 136 will be returned and
not an error message. This is one of the drawbacks of the simple LOOKUP function. Other
reference functions can be used to find only an exact match, but those will not be covered in this
course. You may read about these functions using the Help feature in Excel.
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EXERCISE 1.9-1 REFERENCE FUNCTIONS: PRICING COPIES
A
1
2
3
4
5
6
7
8
B
The Lookup Table for Sliding-Scale Prices:
Number of copies
Price per copy
1
10
100
200
500
1000
Pricing!
0.07
0.06
0.05
0.04
0.03
0.02
9
10
11
Copies Made:
Total Cost:
12
3
10
200
1001
13
14
15
16
A
1
B
C
D
Delivery charges
Delivery!
2
3
4
5
1. Write a formula in cell B13 that can be copied down the column to determine the total cost of
making copies. The number of copies to be made is listed in Column. A.
2. The company also offers delivery. Their delivery charges are as follows:

For orders under $5, there is a $5 delivery fee.

Orders at least $5 but smaller than $20 there is a $7 delivery fee.

Orders of $20 or more are delivered free of charge.
Set up a reference table on the Delivery! worksheet so that you can write a reference function to
calculate the delivery cost for each order. Organize the table in a horizontal format.
3. Write a formula that can be copied down to calculate Delivery Cost in cell C13. Use the
reference table you created in question 2.
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EXERCISE 1.9-2 REFERENCE FUNCTIONS: GRADEBOOK
Sheetname: Grades1!
Sheetname: Grades2!
A
1
2
A
B
C
D
E
700
A
550
B
400
C
300
D
E
0
3
5
4
6
total pts
4
3
6
0
5
F
300
D
400
C
A
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
550
B
B
last
name
Mouse
Duck
Bird
Runner
Cat
Dog
Coyote
Mouse
Pig
Panther
Doright
Bunny
Boop
Duck
first
name
Mickey
Donald
Tweety
Road
Felix
Goofy
Wiley
Minnie
Porky
Pink
Dudley
Buggs
Betty
Daffy
700
A
C
B
1
2
7
8
D
E
F
Midterm 1 midterm 2 final total
125
180 340
645
85
120 200
405
99
199 299
597
148
235 388
771
15
25
39
79
75
150 200
425
106
217 190
513
4
150 150
304
140
240 390
770
66
177 288
531
135
200 322
657
90
182 317
589
142
210 122
474
51
222 333
606
0
300
400
550
700
grade
F
D
C
B
A
G
H
% of
final
total
grade
81%
B
51%
C
75%
B
96%
A
10%
F
53%
C
64%
C
38%
D
96%
A
66%
C
82%
B
74%
B
59%
C
76%
B
16
17 max possible points
150
250
400
800
Sheetname: scores!
Use cell references whenever possible in your formulas:
1. Write a formula in cell scores!G2 that can be copied down the column to determine the
percent of total possible points Mickey Mouse earned.
2. Write a formula in cell scores!H2 that can be copied down the column to determine Mr.
Mouse’s final letter grade. Use a reference function and the grading scale on sheet Grades1!.
3. Write another formula in cell scores!H2 that can be copied down the column to determine Mr.
Mouse’s final letter grade. Use a reference function and this time use the grade listing on sheet
Grades2!.
4. How could you solve this problem without using a reference function?
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EXERCISE 1.9-3 REFERENCE FUNCTIONS: SALES ORDER PRICING
A
Disc!
1
2
3
4
5
6
7
8
9
B
Company
ABC Inc.
DEF Inc.
GHI Corp.
LLL Ind.
NYPD Inc.
PQ Ltd.
RFG Inc.
XYZ Inc.
C
City
Columbus
Philadelphia
Scranton
Long Island
Brooklyn
Warren
Columbus
Cleveland
D
E
Discount Discount
A
B
State
OH
5%
8%
PA
5%
10%
PA
7%
10%
NY
7%
15%
NY
5%
12%
OH
5%
10%
OH
7%
8%
OH
6%
8%
A
D
Total cost
Customer Sales
w/o
Amount Ship Cost Discount
1 Name
3
1000
5%
4
100
10%
5
1
20%
C
E
F
Total Cost
Shipping Cost
with Discount >$25
2 ABC Inc.
345 $
34.50
$
379.50
$
349.14
TRUE
3 DEF Inc.
92 $
18.40
$
110.40
$
104.88
FALSE
4 ABC Inc.
2000 $ 100.00
$ 2,100.00
$
1,932.00
TRUE
32 $
6.40
$
38.40
$
36.48
FALSE
6 RFG Inc.
99 $
19.80
$
118.80
$
110.48
FALSE
7 DEF Inc.
101 $
10.10
$
111.10
$
105.55
FALSE
$ 3,360.00
$
3,091.20
TRUE
5 NYPD Inc.
8 ABC Inc.
A
B
1 Shipping Table #1
sale
percent
shipping
2 amount
B
3200 $ 160.00
discount!
sales!
A
1 Shipping Table #2
2 sales amount
3 percent shipping
ship1!
B
C
D
1
100
1000
20%
10%
5%
ship2!
Above are some worksheets you have prepared to keep track of customer sales. The worksheet
sales! lists each sale made by your company. It will be your job to calculate the shipping costs
and factor in the appropriate discounted sales price for each sale. Shipping charges from $1 to
$99.99 are 20% of the total sale, from $100 to $999.99 shipping charges are 10% of the total
sale, and over $1000 are 5% of the total sale. Each company has negotiated different discount
rates for discount types A and B as given on sheet discount!. Discount A is applied to sales
under $200. Discount B is applied to sales of $200 and above. Discounts are calculated based
total cost w/o discount (sales plus shipping) that you will calculate in column D.
1. If you were to use a reference function in cell sales!C2 to calculate the shipping cost of the
$345 sale (cell sales!B2), would you want to use the data on sheet ship1! as the reference table or
the data on sheet ship2! as the reference table? Why?
2. Using a LOOKUP function, write a formula in cell sales!C2 that can be copied down the
column to calculate the shipping cost of the corresponding sale in that row.
3. What other method can be used to solve question #2? Is this method better or worse? Why?
4. Write a formula in cell sales!D2 that can be copied down the column to calculate the total cost
before discounts (list price plus shipping).
5. Write a formula in cell sales!E2 that can be copied down the column to determine the
discounted price of the order. Remember that discounts are based on a company’s negotiated
discount rate and the total cost of the order (discount A for <$200 or discount B for >=$200).
6. Your competitor charges a $25 flat shipping rate per order. Write a formula (True/False) in
cell sales!F2 to determine if your customer paid more than $25 for his/her shipping.
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EXERCISE 1.9-4 LOOKUP FUNCTIONS: – CHAPTER REVIEW –
The three spreadsheets on the following page are all worksheets in a single workbook. The
worksheet named Prod! lists product information (shipping time, cost, and shipping cost) by
product number. The worksheet named Ship! is a table of shipping costs for the corresponding
product costs. The worksheet named Order! is a list of customer orders (one item type per
order) and the order quantity.
1. Write a formula in cell Prod!D3 using a reference function to calculate the shipping cost for
product 0001. Write the formula so that it can be copied down the column.
2.
Write a formula in cell Order!D3 to calculate the total cost of this order (product costs and
shipping costs). Write the formula so that it can be copied down the column.
3. Write a formula in cell order!G3 to determine (true/false) if the shipment was late. A
shipment is late if it took more that the required number of shipping days to be received.
Write the formula so that it can be copied down the column.
4. Is it possible to write a LOOKUP function in cell Order!G20 to determine the customer name
of the customer with the lowest value order? Why or why not?
5. Write a formula in cell Prod!D3 using a nested if function to calculate the shipping cost for
product 0001. Write the formula so that it can be copied down the column.
A
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
B
Product Information
Shipping
Product Days
ID
Required
0001
0010
0011
0012
0013
0023
0032
0034
0043
0045
0067
0078
0089
C
1
2
7
4
3
7
3
3
4
5
1
6
7
D
A
E
Shipping
Product Cost per
Costs
item
$
25
D3
$
15
$
97
$
65
$
89
$
85
$
76
$
48
$
58
$
32
$
64
$
64
$ 189
1
Product
2 Customer Number
3 Fraiser
0045
4 Johnson
0067
5 Jordon
0001
6 Chamberlain 0012
7 Reed
0023
8 Monroe
0034
9 Bird
0089
10 Barry
0032
11 Lucas
0043
12 Bradley
0010
13 DeBusher
0011
14 Rodman
0078
15 Malone
0013
Product ID
0001
0010
0011
0012
0013
0023
0032
0034
0043
0045
0067
0078
0089
Prod!
A
1
Product Cost
3 Shipping Cost
2
B
C
D
E
F
B
Total
Order
QTY Cost
1 D3
1
1
1
2
3
2
3
1
1
4
1
1
H
C
Shipping Costs
0 $
50 $
$
3 $
5 $
D
Receipt
Ship Date Date
Late?
2/8/98
2/12/98 G3
2/8/98
2/16/98
2/8/98
2/9/98
2/8/98
2/15/98
2/8/98
2/9/98
2/8/98
2/11/98
2/8/98
3/1/98
2/8/98
2/14/98
2/8/98
2/13/98
2/8/98
2/15/98
2/8/98
2/10/98
2/8/98
2/9/98
2/8/98
2/21/98
E
75 $
7 $
Customer
Fraiser
Johnson
Jordon
Chamberlain
Reed
Monroe
Bird
Barry
Lucas
Bradley
DeBusher
Rodman
Malone
Order!
100
9
Ship!
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G
Customer Orders
Page 119