Chapter 10
Graphs, Good and Bad
Chapter 10
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Thought Question 1
What is confusing or misleading about the
following graph?
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Interest Rate
20
19
18
17
16
15
Household
Bank
Central
Bank
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Average
Bank
CHOICE
VISA
2
A picture is worth a thousand words
• The end of 20th century was great for the U.S.
stock market.
• The following figure shows the percentage
increase or decrease in each year from 1971 to
2003.
• For example, in 1973 stocks lost 14.7% of their
value, and another 26.5% in 1974. But starting in
1982, stocks went up in 17 of the next 18 years,
often by a lot.
• Stocks fell from 2000 to 2002, then rebounded in
2003.
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Figure 10.8 Percentage increase or decrease in the S&P 500 index of common stock
prices, 1971 to 2003. (This figure was created using the SPSS software package.)
A picture is worth a thousand words
• The next figure shows how to get rich.
• If you had invested $1,000 in stocks at the end of 1970,
the graph shows how much money you had at the end
of each year.
• After 1974, your $1,000 was down to $853, and at the
end of 1981, it had grown to only $2145. Only 7.2% per
year.
• By the end of 1999, the money market had turned your
$1,000 into $36,108.
• Unfortunately, during the next three years stocks lost
value, and by the end of 2002, your $36,108 had
declined to $22,532.
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Figure 10.9 Value at the end of each year, 1970 to 2003, of $1000 invested in the S&P
500 index at the end of 1970. (This figure was created using the SPSS software package.)
Example: What makes a clear table?
• The following table presents the data for people aged
25 years and over.
Level of education
Number of persons
(thousands)
Percent
Level of education
27,896
14.5
High school graduate
60,898
31.7
Some college, no degree
32,611
17.0
Associate’s degree
16,760
8.7
Bachelor’s degree
35,153
18.3
Advanced degree
18,567
9.7
Total
191,84
100.0
Source: Census Bureau, Educational Attainment in the US: 2006
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Class Make-up on First Day
(Summer 2002)
Data Table
Year
Count
Percent
Freshman
18
41.9%
Sophomore
10
23.3%
Junior
6
14.0%
Senior
9
20.9%
Total
43
100.1%
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Example: What makes a clear table?
• The table is clearly labeled so that we can see
the subject of the data at once.
• Labels within the table identify the variables
and state the units in which they are
measured.
• The source of the data appears at the bottom
of the table.
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Roundoff errors
• Let us check this table for consistency. The
total number of People should be
27,896 + 60,898 +32,611 + 16,760 +35,153+18,567 =
191,885 (thousands)
• The table gives the total as 191,884.
• Each entry is rounded to the nearest
thousand. The rounded entries do not always
add to the total, which is rounded separately.
• Such discrepancies will be referred to as
roundoff errors, and will be with us from now
on.
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Distribution
• Tells what values a variable takes and how
often it takes these values
• Can be a table, graph, or function
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Pie Chart
Figure 10.2 Pie chart of the distribution of level of education among persons aged 25
years and over in 2006. (This figure was created using the Minitab software package.)
Bar Graph
Figure 10.3 Bar graph of the distribution of level of education among persons aged 25
years and over in 2006. (This figure was created using the Minitab software package.)
Pie Chart
Class Make-up on First Day
Senior
20.9%
Freshman
41.9%
Junior
14.0%
Sophomore
23.3%
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Bar Graph
Class Make-up on First Day
45.0%
41.9%
40.0%
35.0%
Percent
30.0%
23.3%
25.0%
20.9%
20.0%
14.0%
15.0%
10.0%
5.0%
0.0%
Freshman
Sophomore
Junior
Senior
Year in School
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• A categorical variable places an individual into
one of several groups or categories.
• A quantitative variable takes numerical values
for which arithmetic operations such as adding
and averaging make sense.
• To display the distribution of a categorical
variable, use pie chart or a bar graph.
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The Effect of Hypnosis on the
Immune System (from Ch.1)
• Easy or difficult to achieve
categorical
hypnotic trance
• Group assignment
quantitative • Pre-study white blood cell count
• Post-study white blood cell count
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Weight Gain Spells Heart
Risk for Women (from Ch.1)
quantitative
• Age in 1976
• Weight in 1976
• Weight at age 18
categorical
• Incidence of coronary heart disease
• Other: smoking, family history,
menopausal status, post-menopausal
hormone use.
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Line Graphs
•
•
•
•
•
A line graph shows behavior over time.
Time is always on the horizontal axis.
Variable you measured is on the vertical axis.
Look for an overall pattern (trend).
Look for patterns that repeat at known regular
intervals (seasonal variations).
• Look for any striking deviations that might
indicate unusual occurrences.
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Price of gasoline
Figure 10.6 A line graph of the average cost of regular unleaded gasoline each week
from January 3, 2000, to January 21, 2008. (Data from the Bureau of Labor Statistics.
This figure was created using the Minitab software package.)
Beware of Pictograms
Figure 10.5 A pictogram. This
variation of a bar graph is
attractive but misleading.
(Copyright © 1971 by Time, Inc.
Reproduced by permission.)
Watch the scales!
Figure 10.7 The effect of changing the scales in a line graph. Both graphs plot the same data,
but the right-hand graph makes the increase appear much more rapid. (These figures were
created using the SPSS software package.)
Keep it simple!
Figure 10.10 Chart junk: this graph is so cluttered with unnecessary ink that it is hard
to see the data.
Organize!
Figure 10.11 Percentage of gross wage earnings paid in income tax and employee
Social Security contributions in eight countries in 2006. Changing the order of the
bars has improved the graph in Figure 10.4. (This figure was created using the
Minitab software package.)
Making Good Graphs
• Title your graph.
• Make sure labels and legends describe
variables and their measurement units. Be
careful with the scales used.
• Make the data stand out. Avoid distracting
grids, artwork, etc.
• Pay attention to what the eye sees. Avoid
pictograms and tacky effects.
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Key Concepts
•
•
•
•
•
•
Categorical and Quantitative Variables
Distributions
Pie Charts
Bar Graphs
Line Graphs
Techniques for Making Good Graphs
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Exercise 10.3
• Lottery sales. States sell lots of lottery tickets.
The following table shows where money comes
from in the state of Indiana. Make a bar graph
that shows the distribution of lottery sales by
type of game. Is it also proper to make a pie
chart of these data? Explain.
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Indiana state lottery sales by type of game, 2006
Game
Sales(millions of dollars)
Scratch-off
504.9
Pull Tab
16.7
Powerball
159.8
Hoosier Lotto
65.6
Daily 3/4
59.4
Lucky 5
7.6
Mix and Match
1.7
TV Bingo
0.5
Raffle
0.1
Total
816.4
Source: State Lottery Commission of Indiana, 2006
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Exercise 10.4
• Check the previous table for consistency. That
is, what is the sum of the amounts spent on
the seven types of games? Is it exactly equal
to the total given in the table?
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Exercise 10.6
• We pay high interest. The following figure
shows a graph taken from an advertisement
for an investment that promises to pay a
higher interest rate than bank accounts and
other competing investments.
• Is this graph a correct comparison of the four
interest rates?
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Figure 10.12 Comparing interest rates.
Exercise 10.8
• Murder weapons. The Statistical Abstract of
the United States, 2008 reports FBI data on
murders for 2005. In that year, 50.5% of all
murders were committed with handguns,
17.3% with other firearms, 12.8% with knives,
6.0% with a part of the body (usually with
hand or feet), and 4.1% with blunt objects.
• Make a graph to display these data. Do you
need an “other methods” category? Why?
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Exercise 10.9
• The cost of tomatoes. The following graph is a line graph of
the average cost of tomatoes each month from January
1997 to December 2007. These data, from the Bureau of
Labor Statistics’s monthly survey of retail prices, are the
price in dollars and cents per pound.
a) The graph shows seasonal variation. How is this visible in
the graph? Why would you expect the price of tomatoes to
show seasonal variation?
b) What is the overall trend in tomato prices during this
period, after we take account of the seasonal variation?
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Figure 10.14 The price of tomatoes, January 1997 to December 2007.
(This figure was created using the Minitab software package.)
Exercise 10.14
• A bad graph? The following figure shows a
graph that appeared in the Lexington (Ky.)
Herald-Leader on October 5, 1975. Discuss the
correctness of this graph.
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Figure 10.16 A newspaper’s graph
of the value of the British pound.
Exercise 10.26
• Accidental deaths. In 2004 there were 112,012 deaths
from accidents in the U.S. Among these were 44,933
deaths from motor vehicles accidents, 20,950 from
poisoning, 3308 from drowning, 3229 from fires, and
649 from firearms.
• Find the percentage of accidental deaths from each of
these causes, rounded to nearest percent. What
percentage of accidental deaths were due to other
causes?
• Make a well-labeled graph of the distribution of causes
of accidental deaths.
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