CHAPTER 1 Picturing Distributions with Graphs
Individuals are the objects described by a set of data. Individuals may be people, but they may also be
animals or things eg dogs, schools, years
A variable is a characteristic of an individual. A variable might vary from one individual to another. eg
hair colour of dog, age of school, amount spent on healthcare in a year
Examples:
Exercise 1.11 page 31 Health Care spending
1.11Health Care Spending. Table 1.3 shows the 2015 per capita total expenditure on
health in 35 countries with the highest gross domestic product in that year.12 Health expenditure
per capita is the sum of public and private health expenditure (in PPP, international $) divided
by population. Health expenditures include the provision of health services, family-planning
activities, nutrition activities, and emergency aid designated for health but exclude the
provision of water and sanitation.
HEALTH
One individual is one _____
The variable is ______
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Exercise 1.36 page 40 Child mortality rates
1.36Child mortality rates. Although child mortality rates have dropped by more than 50% since 1990, in 2015 it was
still the case that 5.4 million children under five years old died in 2017. The mortality rates for children under five
varied from 2.1 per 1000 in Slovenia to 127.2 per 1000 in Somalia. The data set is too large to print here, but here are
the data for the first five countries:
One individual is one _____
The two variables are ______
Exercise 1.34 page 39 Food oils
1.34Food oils and health. Fatty acids, despite their unpleasant name, are necessary for human health. Two types of
essential fatty acids, called omega-3 and omega-6, are not produced by our bodies and so must be obtained from our
food. Food oils, widely used in food processing and cooking, are major sources of these compounds. There is some
evidence that a healthy diet should have more omega-3 than omega-6. Table 1.4 gives the ratio of omega-3 to omega-6
in some common food oils. Values greater than 1 show that an oil has more omega-3 than omega-6.
TABLE 1.4 Omega-3 fatty acids as a fraction of omega-6 fatty acids in
food oils
Oil
Ratio
Oil
Ratio
Perilla
5.33
Flaxseed
3.56
Walnut
0.20
Canola
0.46
Wheat germ
0.13
Soybean
0.13
Mustard
0.38
Grape seed
0.00
Sardine
2.16
Menhaden
1.96
Salmon
2.50
Herring
2.67
Mayonnaise
0.06
Soybean, hydrogenated
0.07
Cod liver
2.00
Rice bran
0.05
Shortening (household)
0.11
Butter
0.64
Shortening (industrial)
0.06
Sunflower
0.03
Margarine
0.05
Corn
0.01
Olive
0.08
Sesame
0.01
2
Shea nut
0.06
Cottonseed
0.00
Sunflower (oleic)
0.05
Palm
0.02
Sunflower (linoleic)
0.00
Cocoa butter
0.04
One individual is one _____
The variable is ______
Exercise 1.37 page 40 Fur seals
1.37Fur seals on St. Paul Island. Every year, hundreds of thousands of northern fur seals return to their haul-outs in the
Pribilof Islands in Alaska to breed, give birth, and teach their pups to swim, hunt, and survive in the Bering Sea. U.S.
commercial fur sealing operations continued on St. Paul until 1984, but despite a reduction in harvest, the population of
fur seals has continued to decline. Possible reasons include climate shifts in the North Pacific, changes in the
availability of prey, and new or increased interaction with commercial fisheries that increase mortality. Here are data
on the estimated number of fur seal pups born on St. Paul Island (in thousands) from 1979 to 2018, where a dash
indicates a year in which no data were collected:
One individual is one _____
The variable is ______
Note: The four data sets above (health care data set, Child mortality data set, etc) are all raw data,
meaning that we have a list of the individuals and information for each individual is presented.
When we have raw data, we can identify the individuals by moving from one line in Minitab to another.
Each new line has a new individual. In the next example, we have a summarized data set. We do not
have a list of individuals with information alongside. The data are already summarized into a table.
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Exercise 1.25 page 36 Car colour data
1.25What color is your car? The most popular colors for cars and light trucks vary with region, type of vehicle, and
over time. In North America, silver and white are the most popular choices for midsize cars, siler and black for
convertibles and coupes, and white for light trucks. Despite this variation, overall white remains the top choice
worldwide for the eighth consecutive year, increasing its lead by 2% over the previous year. Here is the distribution of
the top colors for vehicles sold globally in 2018:
One individual is one _____
The variable is ______
Two types of variables.
A categorical variable is a qualitative characteristic that describes an individual in a non-numeric way.
eg Gender of person, opinion of person, primary colour of dog. The information recorded is usually
expressed as words, not numbers.
A quantitative variable is a characteristic that describes an individual in a numeric way. eg height of
person, weight of dog, speed of car, number of children per family. The numbers must have numeric
meaning—it must make sense to form an average. Examples of numeric variables that have no numeric
meaning are
 student ID number (it makes no sense to form an average student number)
 gender, where male = 1 and female =0. It makes no sense to form an average of the numbers
because they are labels of categories.
 Opinion, where SD = 1, D = 2, N = 3, A = 4, SA = 5. It makes no sense to form an average of the
numbers because there is no concept of distance between S and SD, between D and N, etc. the
numbers are merely labels. Also, a 2 from one person might be quite different from a 2 from
some-one else, because people differ in their psychological attitudes. Some people feel strongly
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about everything and they will answer SA or SD to everything. Others are more laid-back, and
they will never use SA or SD, even if they feel strongly.
Examples:
Exercise 1.11 page 31 Health care spending
The variable is (circle correct) categorical / quantitative
Exercise 1.36 page 40 child mortality
The variable ___________ is (circle correct) categorical / quantitative
The variable ___________ is (circle correct) categorical / quantitative
Exercise 1.34 page 39 Food oils
The variable ___________ is (circle correct) categorical / quantitative
Exercise 1.37 page 40 Fur seals
The variable ___________ is (circle correct) categorical / quantitative
Exercise 1.25 page 36 Car colour data
The variable is (circle correct) categorical / quantitative
Distributions of variables
The distribution of a variable gives the possible values of the variable along with how often these
values occur. Note that value can refer to a possible number or a possible category. Eg Suppose the
variable is gender. The possible values might be female, male, other
Distributions of variables are sometimes presented in tables. eg Exercise 1.25 page 36 Car colour data.
The table gives the distribution of car colours.
Distributions of categorical variables are displayed in bar charts or pie charts. To describe the
distribution of a categorical variable, we need to write about
 the most common category,
 the least common category and
 something (anything) else of interest.
Distributions of quantitative variables are displayed in histograms, dot plots, stem-and-leaf plots or boxand-whisker plots. To describe the distribution of a quantitative variable, we need to write about the
centre, spread, shape and outliers.
Example: (Make bar chart and describe it.)
We will make a table to show the distribution of eye colour of people in a room.
One individual is one ________
The variable is (name the variable) _________
What sort of variable is this? (Hint: categorical or quantitative?)
Eye Colour
Number of people
5
Blue
Brown
Green
Grey
Hazel
8
15
6
1
4
Next: Use Minitab to make a bar chart to display the distribution of eye colour of people in the room
now. First type the table above into your Minitab worksheet.
Then
Graph> bar chart> Bars represent> values from a table> simple> graph variable Select number of
people>categorical variable Select eye colour>OK
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Chart of Number of people
16
14
Number of people
12
10
8
6
4
2
0
Blue
Brown
Green
Grey
Hazel
Colour
Note: Instead of graphing the number of individuals, we can graph the percentage of individuals.
Please experiment at home to make the bars different colours and have different fill patterns. In the
future, when you are presenting data to an audience, remember that your audience will appreciate a
colourful picture much more than a boring table of numbers.
To edit a graph in Minitab (eg change the title of the graph, the names of the axes, the colours of the
bars), please double-click on the graph and then double-click on the item you want to change. To change
the colour of a particular bar, point to the bar and click once. You’ll see tiny boxes pop up at the corners
of all the bars. Click again and the tiny boxes will be at the corners of the bar you are pointing to. You
are now ready to edit that bar. Right-click and select Edit bar. Choose custom. Then select your fill
pattern and background colour. Hit OK when you are done editing your graph.
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To copy a Minitab graph (eg to Word, Excel, Powerpoint), please click on the arrow top right of the
graph. Select copy graph. The graph will be under your mouse. Open up your Word doc and paste the
graph wherever you want it.
To print a Minitab graph, please click on the arrow top right of the graph. Select Print graph.
To save your Minitab graph, please click on the arrow top right of the graph. Select Save As.
Distribution of eye colour
50
Percent of people
40
30
20
10
0
Blue
Brown
Green
Grey
Hazel
Colour
Next: Describe the distribution of eye colour. This requires us to read the graph. We need to write
about the most common category, the least common category and anything else of interest.
The most common eye colour is ________. ____% of people in the room have _______ eyes.
The least common eye colour is ________. ____% of people in the room have _______ eyes.
Something else of interest (try to make a comparison):
Note: A pie chart can be used to describe the distribution of a categorical variable if we have included
each individual exactly once and the percentages add up to 100%. Another way of saying this is that the
categories are all parts of a single “pie”.
Example: (Make a pie chart and describe it.) Can we make a pie chart of the eye colour data? Yes /
No (circle correct)
Why or why not?
If so, make a pie chart using Minitab.
Graph> pie chart> Chart values from a table> categorical variable Select eye colour> summary variables
Select number of people>OK
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Pie Chart of Colour
Category
Blue
Brown
Green
Grey
Hazel
Now use the pie chart to describe the distribution of eye colour of people in the room now. Change the
colours of the slices by clicking on each slice. Hover over each slice in Minitab to see the
percentages.
Solution:
The most common eye colour is brown. 44% of people in the room have brown eyes.
The least common eye colour is grey. 3% of people in the room have grey eyes.
Similar percentages of people in the room have green eyes and blue eyes: 24% have blue eyes and 18%
have green eyes.
Notice that the description of the distribution of eye colour is the same using the pie chart and bar chart.
Can we make a pie chart of the car colour data (exercise 1.25, page 37)? Yes / No (circle correct)
Why or why not?
Next: Pictures to describe the distributions of quantitative variables. The four possible pictures are
dot-plot, histogram, stem-and-leaf plot, box-and-whisker plot. To describe the distribution of any
quantitative variable, we need to describe the centre, spread, shape, outliers.
Dotplots: A dotplot is drawn by placing a dot along a line to show the size of each reading.
Exercise 1.11 p 31 data only: Use Minitab to make a dot-plot to show the distribution of the amount
spent in the health care data. Describe the distribution of the amount spent on health care.
Graph>dotplot>one Y simple> Graph variables Select Dollars > OK
9
Dotplot of Dollars
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
Dollars
Centre: The centre is the value of the variable that has half of the individuals below it and half of the
individuals above it.
Think of lining up the countries in order, so that the country with smallest amount spent is first and
the country with the largest amount spent is last. What is the amount spent by the country in the middle
of the line-up?
To find the location of the middle country, calculate 𝑛+1
, where n is the number of individuals in the
2
data set.
35+1
Here, n = 35 (how do you know?) so 𝑛+1
= 2 = 18 Now count to the 18th dot, starting from the left or
2
right. Country number 18 is at about $2600 in the dot-plot.
Now put this number into a sentence: The typical amount spent is $_________
Note: If we get a whole number, the centre is the amount spent by the country in that position. (Here,
country 18 is in the middle, so the centre is the amount spent by country 18 in the ordered list.)
If we don’t get a whole number, the centre is the average of the amounts spent by the two countries on
𝑛+1
either side of the number we get when we calculate 2 .
10+1
(eg If we had 10 countries, then 𝑛+1
= 2 = 5.5 so there are two countries in the middle: the 5th and
2
6th. We’d average the amounts spent by the 5th and 6th countries in the sorted list. )
Spread: The spread tells us how much the variable varies.
Spread = Max minus min =
Now put this number into a sentence: The amounts spent are spread over $____
Outliers: Generally, an outlier is an individual that does not follow the overall pattern of the data.
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In a distribution, an outlier is an individual whose value is lot more or a lot less than the others.
In histograms, stem-plots and dot-plots, outliers can be identified because there is a gap between certain
individuals and the others.
Look at the dot-plot. Comment on outliers in the health care data:
Shape: The shape of a distribution is either symmetric or skewed. Skewed means lop-sided or nonsymmetric.
Positive skewness is the same as being skewed to the right. Negative skewness is the same as being
skewed to the left. Look at the long tail!!
Symmetric:
50% of the area
is to the left of
the middle
Bottom 50%
50% of the total
area is to the right
of the middle
Top 50%
Note: Cut the area in half by eye. In a symmetric distribution, the spread of the lower 50% (blue line
with arrows) is approximately the same as the spread of the top 50% (red line with arrows).
Skewed to the right: The distribution has a long tail on the right.
50% of
area
Bottom 50%
50% of
area
Top 50%
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Note: Cut the area in half by eye. In a distribution that is skewed to the right, the spread of the lower
50% (blue line with arrows) is less than the spread of the top 50% (red line with arrows).
Skewed to the left: The distribution has a long tail on the left.
50% of
area
50% of
area
Bottom 50% Top 50%
Note: Cut the area in half by eye. In a distribution that is skewed to the left, the spread of the lower 50%
(blue line with arrows) is more than the spread of the top 50% (red line with arrows).
Note: Please exclude outliers when deciding about shape. In particular, outliers do not cause
skewness! If you see outliers, please do NOT create a long tail to include the outliers.
Use the dot-plot to find the shape: First, find the centre, then compare the spread to the left of the centre
with the spread to the right of the centre. Which side is more spread out?
The distribution of the amounts spent on health care is (circle correct) symmetric / skewed to the left /
skewed to the right because the spread of the top 50% of the amounts spent is (circle correct) more than /
less than /about the same as the spread of the bottom 50% of the amounts spent.
Exercise 1.11 page 31 Health care spending (Make a histogram and describe it.)
1.11Health Care Spending. Table 1.3 shows the 2015 per capita total expenditure on
health in 35 countries with the highest gross domestic product in that year.12
12
Use Minitab to make a histogram to show the distribution of amounts spent on health care.
Graph>histogram>simple> Graph variables Select Dollars > OK
Histogram of Dollars
12
10
Frequency
8
6
4
2
0
0
2000
4000
6000
8000
10000
Dollars
13
Double- click on the names of the axes to change the names. Double-click on the numbers to change the
tick marks. Select binning to change from midpoint to cut point. Click on a bar twice to change the fill
pattern and colour (edit bar)
Distribution of amount spent on healthcare in the 35 richest countries
9
Number of countries
8
7
6
5
4
3
2
1
0
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
Amount spent on healthcare
The height of a bar is always a whole number because the height is the number of individuals in that
bin/group. To find the number of individuals in the data set, add up all the heights.
Read the histogram:
How many of these countries spent more than $3000 on health care in 2015?
What percentage of these countries spent less than $2000 on health care in 2015?
Approximately what percentage of countries spent more than $3500 on health care in 2015?
Next: Use the histogram to describe the distribution of amounts spent on health care in 2015 by the 35
countries that had the highest GDP in 2015.
Centre: To find the location of the middle country, calculate 𝑛+1
, where n is the number of individuals
2
in the data set.
35+1
Here, n = 35 (how do you know?) so 𝑛+1
= 2 = 18
2
th
Now count to the 18 country, starting from the left or right. (Add up to heights of the bars!) Country
number 18 is somewhere between $2000 and $3000 in the histogram (we can’t tell exactly where, so
let’s guess about $2800 in the histogram. (Centre=$2800)
Now put this number into a sentence: The typical amount spent is $_________
Spread: To find the spread, spread = max minus min = 10,000 minus 0 = 10,000.
The amounts spent on health care in 2015 by these countries are spread over $_______.
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Shape: The distribution of the amount spent on health care is (circle correct) symmetric / skewed to the
left / skewed to the right because the spread of the top 50% of the amounts spent is (circle correct) more
than / less than /about the same as the spread of the bottom 50% of the amounts spent.
 Comment on outliers in the health care data.
One country spent a lot more than all the other countries. This country spent approx. $9500 on health
care.
Note: People describing shapes of distributions often talk about modes. A mode is a value that occurs
more frequently than other values nearby. Visually, a mode appears as a peak. All of the distributions
above are uni-modal, meaning that they have one peak. A bi-modal distribution has two peaks. A
multi-modal distribution has many peaks.
Examples: What are the shapes of the 8 distributions below?
A is
B is
C is
D is
E is
F is
G is
H is
Stem-and-leaf plots.
Stem-and-leaf plots (a.k.a. stem-plots) are used to display distributions of quantitative variables.
Describe the distribution as you would in a histogram: centre, spread, shape and outliers.
Example: Use Minitab to make a stem-plot to show the distribution of the amount spent on health care
Graph>stem and leaf> Graph variables Select Dollars > OK
15
What do you notice about this picture? (Compare it with the histogram.)
Amount spent on health care (35 richest countries in 2018)
9
8
Number of countries
7
6
5
4
3
2
1
0
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
Amount spent on health care ($)
In order to understand how a stem-plot works, let’s do a simple example by hand.
Example: The Age data. The data comprise the ages (years) of 10 people sitting on a bus.
21 60 66 70 71 73 74 76 84 90
Make a stem plot by hand.
16
First, divide each number into a leaf (right most digit) and a stem (the remaining digits) eg the number
21 has stem 2 and leaf 1.
The stems needed are between 2 and 9. Write them down the page, and then attach the leaves to the
appropriate stem:
Use Minitab to make a stem plot for the age data. You’ll need to type the data into the worksheet.
From now on, please always use Minitab to draw stem-plots.
Leaf units. The leaf unit tells us the units for the data. eg If the leaf unit is 10 then the numbers are tens.
If the leaf unit is 100 then the numbers are in hundreds.
When reading a number from a stemplot, put the stem and leaf together and multiply by the leaf unit.
eg If the stem is 6, the leaf is 2 and the unit is 100, the number is 62*100=6200.
If the stem is 60, the leaf is 2 and the unit is 10, the number is 602*10=6020.
If the stem is 6, the leaf is 2 and the unit is .01 the number is 62*.01=0.62
Example: Use the stem-plot to describe the distribution of the amounts spent on health care in 2015 by
the 35 countries that had the highest GDP in 2015.
17
𝑛+1
35+1
To find the centre, calculate 2 = 2 = 18. Now count to leaf number 18. Leaf (=country) number 18
has leaf 5 and stem 2. The leaf unit is 100. So country number 18 spent $2500 on health care.

Typically, the 35 countries that had the highest GDP in 2015 spent $________on health care in
2015.
To find the spread, spread = max minus min = 9500 minus 100 = 9400

The amounts spent on health care in 2015 are spread over $_______ .

The distribution of the amounts spent on health care in 2015 is (circle correct) symmetric /
skewed to the left / skewed to the right because the spread of the top 50% of the amounts spent is
(circle correct) more than / less than /about the same as the spread of the bottom 50% of the
amounts spent.
To see the shape, rotate the stem-plot 90 degrees counter-clockwise. Always put the small numbers on
the left hand side.
Notice that “top 50%” refers to the biggest numbers, not the top of the graph! Likewise “bottom 50%”
refers to the small numbers, not the bottom of the graph.

The distribution of the amounts spent on health care in 2015 is (circle correct)
uni-modal / bi-modal / multi-modal because it has _______peak(s).
 Comment on outliers in the health care data.
One country spent a lot more than all the other countries. This country spent $9100 on health care.
Notice that the descriptions using the histogram and the stem-plot are similar. The numbers from the
stem-plot are more accurate than the numbers from the histogram.
Note: Minitab has several internal formulae for identifying outliers. You can invoke one of these if you
select Trim outliers in the stem-plot program.
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Example: Use Minitab’s stem-plot program to identify outliers in the nurses data (ex 1.35 page 39).
Graph>stem and leaf> Graph variables Select Nurses > check Trim outliers>OK
In the output, HI refers to a high outlier (a reading a lot bigger than the others) and LO refers to a low
outlier (a reading a lot smaller than the others.)
Comment on outliers in the Nurses data. One state had a lot more nurses than all the other states. This
state had 1480 nurses per 100,000 people.
Note:
1) The results of reading the different graphs are not exactly the same. This is not a problem
because we need only a general idea of the data.
2) In practice, histograms are used for relatively large data sets while dot plots and stem-plots are
used for relatively small data sets. Dot-plots and stem-plots represent each data point in the graph
so they are not useful or even feasible if the data set is large. Imagine a stemplot with 1000
leaves or a dot plot with 1000 dots! The data sets in this course are mostly in the range of sizes
that any graph can be used.
More examples (do at home!)
1) Describe the distribution of Iowa Tests vocabulary scores (for seventh-graders in Gary, Indiana)
using the histogram at the top of page 26.
2) Refer to Exercise 1.36 on page 40. The data set for this example contains 2 errors. To fix the
data that you get from the textbook: please delete the income level of countries in rows 175 and
211. Type in Low for each. Then make the graphs below.
(a) Describe the distribution of child mortality rates of all the countries in the WHO data base.
Put all the countries together (ie ignore income level) to make one histogram.
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(b) Make side by side histograms to show the distributions of child mortality by income.
Stat>Basic Stats>Display descriptive stats> Variables Select Rate> By variable Select Income>Hit
the Graphs button> Select histogram
Histogram of rate by Income
0
20
40
60
High
80
100
120
Low
20
15
Frequency
10
5
Lower-middle
Upper-middle
0
20
15
10
5
0
0
20
40
60
80
100
120
rate
Panel variable: Income
Time Series plots
A time series is a collection of readings of a variable taken sequentially in time. (eg one reading is
recorded every year, one reading is taken every month, one reading is taken every second.) A time series
plot shows how the variable has changed over time. This course deals with time series in which three
possible features may be seen: trend, seasonality and random fluctuation.
Trend is the overall change in the variable during the time period for which we have data. Trend may be
increasing (if the numbers generally became larger as time passed) decreasing (if the numbers generally
became smaller as time passed) or constant if the numbers fluctuated but did not generally get bigger or
smaller).
Eg increasing trend
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Decreasing trend
Constant trend (no trend)
Seasonality is a repeating pattern that continues throughout the time period for which we have data.
eg
Does this time series have trend as well as seasonality? If so, what sort of trend?
Note: the authors of the book refer to seasonality as cycle because this is how mathematicians describe a
regular repeating pattern. In fact, in statistics, a cycle is a long-term irregular change. For example, we
know that the economy of any country will experience a recession every so often. There is no way of
predicting when a recession will occur because a recession is part of the business cycle which is an
irregular progression.
21
The time series in this course are too short to distinguish between cycle and trend so we will not
consider cycle in this course—only trend and seasonality.
Random fluctuation is seen as irregular short term changes up or down, including spikes. Time series
graphs are never smooth—the line wobbles. This is random fluctuation.
Exercise 1.45 page 43 Housing starts 1.45Housing starts. Figure 1.19 is a time plot of the number of singlefamily homes started by builders each month from January 1990 through July 2019. The counts are in thousands of
homes.
Housing starts is the number of new houses that builders started to build in a given month.
How did the number of new houses change between January 1990 and July 2019?
Trend:
Seasonality:
Exercise 7.42 page 192 Ozone hole.
7.42Ozone hole. The ozone hole is a region in the stratosphere over the Antarctic with exceptionally depleted ozone.
The size of the hole is not constant over the year but is largest at the beginning of the Southern Hemisphere spring
(August–October). The increase in the size of the ozone hole led to the Montreal Protocol in 1987, an international
treaty designed to protect the ozone layer by phasing out the production of substances, such as chlorofluorocarbons
(CFCs), believed to be responsible for ozone depletion. The following table gives the average ozone hole size for the
period September 7 to October 13 for each of the years from 1979 to 2019. (note that no data were acquired in
1995).To get a better feel for the magnitude of the numbers, the area of North America is approximately 24.5 million
square kilometers (km2).
OZONE
22
Make a time series plot to show how the area of the ozone hole has changed..
Graph>Time series plot> simple>For series, select Area
Hit the Time/Scale button and select Time stamp. For time stamp columns, select Year. OK, OK
23
Time Series Plot of Area
30
25
Area
20
15
10
5
0
1982
1986
1990
1994
1998
2002
2006
2010
2014
2018
Year
How did the size of the ozone hole change between 1979 and 2019?
Trend: The ozone hole increased in size from close to 0 million square km in 1979 to about 22 million
square km in 1990. It stayed approximately the same size until around 2005. Between 2005 and 2019 it
has decreased in size to about 18 million square km.
No seasonality.
Lots of random fluctuation.
Note: People often use the word “trend” in everyday speech to describe random fluctuation. This is not
correct. Eg in the ozone data below, it is WRONG to describe the trend as increasing from 1979 to 1980,
then decreasing from 1980 to 1981 then increasing from 1981 until 1985, then decreasing until 1986,
then increasing ….. All of these changes are random fluctuation, not trend!
Note:
1) Bar charts should not be used for time series data
Chart of $ spent on health care
8000
7000
5000
4000
3000
2000
1000
0
2014
2015
2016
2017
2018
2019
Year
Time Series Plot of $ spent on health care
7000
$ spent on health care
$ spent on health care
6000
6500
6000
5500
5000
2014
2015
2016
2017
2018
2019
Year
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2) Time series plots should not be used to describe the distributions of categorical variables.
Time Series Plot of Percentage
35
Percentage
30
25
20
15
10
F
D
C
B
A
Grade
Grade distribution
40
Percentage
30
20
10
0
F
D
C
B
A
Grade
Review exercises for Chapter 1:
Exercises 1.1, 1.3, 1.5, 1.13-1.22, 1.23, 1.27, 1.29*, 1.31, 1.33, 1.35, 1.37, 1.39, 1.41(same
type of graph as in 1.29), 1.43
Abbreviated solutions to all odd-numbered exercises are at the back of the book—p686
onwards. Answers for even-numbered exercises: 1.14(c), 1.16(b), 1.18(b), 1.20(a), 1.22(c)
*Graph>Bar chart>Bars represent values from a table >Select Two way table Cluster >Graph
variables: Select Amazon Google Search >Row labels: Select Age > Table arrangement: Select
Rows are outermost….
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