Section 1.1 Solutions

1.11

The bar chart is shown below. On average, unmet need seems to be greatest at private, rather than public, institutions (especially private for-profit institutions). This makes sense, because public institutions receive financial support from state governments.

A pie chart would be inappropriate for these data because the numbers do not represent parts of a whole (the numbers are averages, not totals, and not all types of institutions are represented).

1.12

The timeplots are shown below. The problems for both companies have decreased each year, with the exception of 2003. Vehicles from Toyota have fewer problems, although General Motors seems to be closing that gap.

1.18

Rounding the data to the nearest 10s digit and splitting the stems gives the following back-to-back stem-and-leaf plots (note: you could have simply trimmed the last digit, rather than rounding):

Fasting Plasma Glucose (mg/dl)

Leaf unit = 10.0

Class		Individual
8	0
431000	1	33
7765555	1	666669
0	2	0022233
76	2	8
	3
6	3

The fasting glucose values for those who got individual instruction are centered slightly higher and have less spread. More people who took the class (rather than individual instruction) were in the target range of 90 to 130 mg/dl.

1.20

The distribution of lengths of words in Shakespeare’s plays is skewed to the right. That is, his plays contain many short words (up to 5 or 6 letters) and fewer long words. To ensure readability, I think most authors would have a skewed distribution of word lengths, although the strength of the skew might vary from author to author.

1.31

Label the graphs A, B, C, and D, moving right across the first row (and then down to the next row). The sex variable and the handedness variable are categorical with two categories; hence the responses to these two variables must be shown in graphs B and C. The discrepancy between the categories of handedness should be more extreme than the discrepancy between the categories of sex (the percentage of left-handers is very small compared to the percentage of right-handers, yet the difference in sex percentages shouldn’t be as large). Hence, the handedness variables must be shown in graph B and the sex variable must be shown in graph C.

The distribution of the heights of college students is typically symmetric within sex. Combining males and females together, the distribution of heights may show a bimodal shape, but it shouldn’t show a skewed shape. On the other hand, it makes sense that the study minute distribution is skewed: there’s a lower boundary (0 minutes) that will be reached by many students (studying very little or not at all – or course this doesn’t happen at Lawrence!), and there will be a longer right tail of a few students who study a ton. Hence, study time must be shown in graph A and height must be shown in graph D.

1.34

Both a stemplot and a histogram of the density measurements are shown below. The stemplot is nice because it shows both the overall shape of the distribution and the individual values. The histogram is nice because it more smoothly shows the distribution. Both graphs show the distribution to be roughly symmetric with a center around 5.4 or 5.5.

Density of Earth

Leaf Unit = 0.01

48 | 8

49 |

50 | 7

51 | 0

52 | 6 7 9 9

53 | 0 4 4 6 9

54 | 2 4 6 7

55 | 0 3 5 7 8

56 | 1 2 3 4 8

57 | 5 9

58 | 5