Chapter 10

Graphs, Good and Bad

Chapter 10 1

Thought Question 1

Chapter 10 2

What is confusing or misleading about the following graph?

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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 stockprices, 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&P500 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.

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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)

Year Count Percent

Freshman 18 41.9%

Sophomore 10 23.3%

Junior 6 14.0%

Senior 9 20.9%

Total 43 100.1%

Data Table

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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Figure 10.2 Pie chart of the distribution of level of education among persons aged 25years and over in 2006. (This figure was created using the Minitab software package.)

Pie Chart

Figure 10.3 Bar graph of the distribution of level of education among persons aged 25years and over in 2006. (This figure was created using the Minitab software package.)

Bar Graph

Class Make-up on First Day

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Freshman41.9%

Sophomore23.3%

Junior14.0%

Senior20.9%

Pie Chart

Class Make-up on First Day

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41.9%

23.3%

14.0%

20.9%

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10.0%

15.0%

20.0%

25.0%

30.0%

35.0%

40.0%

45.0%

Freshman Sophomore Junior Senior

Year in School

Per

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Bar Graph

• 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 hypnotic trance

• Group assignment• Pre-study white blood cell count• Post-study white blood cell

count

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categorical

quantitative

Weight Gain Spells Heart Risk for Women (from Ch.1)

• Age in 1976• Weight in 1976• Weight at age 18

• Incidence of coronary heart disease• Other: smoking, family history,

menopausal status, post-menopausal hormone use.

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quantitative

categorical

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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.

Figure 10.6 A line graph of the average cost of regular unleaded gasoline each weekfrom January 3, 2000, to January 21, 2008. (Data from the Bureau of Labor Statistics. This figure was created using the Minitab software package.)

Price of gasoline

Figure 10.5 A pictogram. This variation of a bar graph is attractive but misleading. (Copyright © 1971 by Time, Inc. Reproduced by permission.)

Beware of Pictograms

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.)

Watch the scales!

Figure 10.10 Chart junk: this graph is so cluttered with unnecessary ink that it is hardto see the data.

Keep it simple!

Figure 10.11 Percentage of gross wage earnings paid in income tax and employeeSocial 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.)

Organize!

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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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

Indiana state lottery sales by type of game, 2006

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 graphof 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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