1. Statistics: Concepts and Controversies Graphs, Good and Bad
Chapter 10
Graphs, Good and Bad
Chapter 10
Chapter 10

2. Statistics: Concepts and Controversies
Thought Question 1
What is confusing or misleading about the following graph?
Chapter 10
Chapter 10

3. A picture is worth a thousand words
Statistics: Concepts and Controversies
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 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.
Chapter 10
Chapter 10

4. Figure 10.8 Percentage increase or decrease in the S&P 500 index of common stock
prices, 1971 to (This figure was created using the SPSS software package.)

5. A picture is worth a thousand words
Statistics: Concepts and Controversies
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.
Chapter 10
Chapter 10

6. 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 (This figure was created using the SPSS software package.)

7. Example: What makes a clear table?
Statistics: Concepts and Controversies
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
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
Chapter 10
Chapter 10

8. 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%
Chapter 10

9. Example: What makes a clear table?
Statistics: Concepts and Controversies
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.
Chapter 10
Chapter 10

10. Statistics: Concepts and Controversies
Roundoff errors
Let us check this table for consistency. The total number of People should be
27, , , , ,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.
Chapter 10
Chapter 10

11. Statistics: Concepts and Controversies
Distribution
Tells what values a variable takes and how often it takes these values
Can be a table, graph, or function
Chapter 10
Chapter 10

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

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

14. Class Make-up on First Day
Statistics: Concepts and Controversies
Pie Chart
Class Make-up on First Day
Chapter 10
Chapter 10

15. Class Make-up on First Day
Statistics: Concepts and Controversies
Bar Graph
Class Make-up on First Day
Chapter 10
Chapter 10

16. Statistics: Concepts and Controversies
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.
Chapter 10
Chapter 10

17. The Effect of Hypnosis on the Immune System (from Ch.1)
Statistics: Concepts and Controversies
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
categorical
quantitative
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Chapter 10

18. Weight Gain Spells Heart Risk for Women (from Ch.1)
Statistics: Concepts and Controversies
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.
quantitative
categorical
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Chapter 10

19. 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.
Chapter 10

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

21. 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.)

22. Watch the scales!
Figure 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.)

23. Keep it simple!
Figure Chart junk: this graph is so cluttered with unnecessary ink that it is hard
to see the data.

24. Organize!
Figure Percentage of gross wage earnings paid in income tax and employee
Social Security contributions in eight countries in Changing the order of the
bars has improved the graph in Figure (This figure was created using the
Minitab software package.)

25. Statistics: Concepts and Controversies
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.
Chapter 10
Chapter 10

26. Statistics: Concepts and Controversies
Key Concepts
Categorical and Quantitative Variables
Distributions
Pie Charts
Bar Graphs
Line Graphs
Techniques for Making Good Graphs
Chapter 10
Chapter 10

27. Statistics: Concepts and Controversies
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.
Chapter 10
Chapter 10

28. Statistics: Concepts and Controversies
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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Chapter 10

29. Chapter 10

30. Chapter 10

31. Statistics: Concepts and Controversies
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?
Chapter 10
Chapter 10

32. Statistics: Concepts and Controversies
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?
Chapter 10
Chapter 10

33. Figure 10.12 Comparing interest rates.

34. Statistics: Concepts and Controversies
Exercise 10.8
Murder weapons. The Statistical Abstract of the United States, 2008 reports FBI data on murders for 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?
Chapter 10
Chapter 10

35. Statistics: Concepts and Controversies
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 These data, from the Bureau of Labor Statistics’s monthly survey of retail prices, are the price in dollars and cents per pound.
The graph shows seasonal variation. How is this visible in the graph? Why would you expect the price of tomatoes to show seasonal variation?
What is the overall trend in tomato prices during this period, after we take account of the seasonal variation?
Chapter 10
Chapter 10

36. Figure 10.14 The price of tomatoes, January 1997 to December 2007.
(This figure was created using the Minitab software package.)

37. Statistics: Concepts and Controversies
Exercise 10.14
A bad graph? The following figure shows a graph that appeared in the Lexington (Ky.) Herald-Leader on October 5, Discuss the correctness of this graph.
Chapter 10
Chapter 10

38. Figure 10.16 A newspaper’s graph
of the value of the British pound.

39. Statistics: Concepts and Controversies
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.
Chapter 10
Chapter 10