3.3 A. the Second and Third Categories Were Combined Into One Category

Chapter 3 Homework

Category Percent Calculation Degrees Toned and Fit 18% .18*360 65 Flabby 55% .55*360 198 Out of Shape 27% .27*360 97

3.2 Segmented Bar Chart

3.3 a. The second and third categories were combined into one category.

c. Pie Chart or Regular Bar Chart

3.5 Either bar chart or pie chart is reasonable here. I would recommend a bar chart, since there are more than four categories. Pie charts are not ideal for data with more than four categories.

3.6 a. Overall score is a numerical variable. Grade is a categorical variable.

b. Each different color in the chart is a segment, which is proportional to the relative frequency of that category.

Your answer for the new assignment of grades may vary. Make sure you are able to defend your answer.

b. Yours may vary. For example, “How were the women to be questions selected?” or “How were the questions worded?”

c. Japan seems to be an outlier here, with its reported percentage of spouses who do not help with housework more than double two of the other countries. The other four countries (France, UK, US and Canada) have results that are more similar to each other, with Canada reporting the least percentage loaf-around husbands. 3.8 a.

b. If frequencies rather than relative frequencies were used, it would be impossible to compare the information. For example, the same percentage of men and women reported themselves into the “lowest 10%” category. But in absolute numbers, nearly twice as many women would be in this category, since there are nearly twice as many women as men in the study. So the two bars would not be the same height.

c. Very few college seniors reported themselves to be below average. “Average” was the most common response for women, and “above average” was the most common for men. The “Top 10%” category seems accurate for women – 10% of women placed themselves in this category. But more than twice as many men – 22% - self-report into the “Top 10%” category.

3.15 10 578 11 79 12 1114 13 001122478899 14 0011112235669 15 11122445599 16 1227 17 1 18 19 20 8 Stem: ones

Leaves: tenths

The typical number of births per thousand is around 14, with a large cluster between 13 and 16. There is one peak. An extreme value of 20.8 is the only value above 17.1 People in Utah had a lot of babies in 2007 for some reason.

3.17 a. 0L 0H 55567889999 1L 0000111113334 1H 556666666667789 2L 0000112223 2H 5 Stem: tens

Leaves: ones

The typical value of households that have only cell phones is 15%

b. West East

998 0H 555789

110 1L 00011134 8766 1H 666

21 2L 00

Stem: tens

Leaves: ones

An average number of homes with only cell phones is about 16 for the Western states, and 11 for the Eastern states. The Western states distribution is symmetrical, while the Eastern states distribution has more lower numbers.

3.19 -1 100 -0 99998888776555555444433222211110 0 000011244577 1 179 2 2 Stem: tens Leaves: ones

b. Break apart each of the above stems into a high and low, such as -0H, -0L, 0L, 0H, etc c. The states with the largest increase in the number of 25-44 year olds working are Arizona, Idaho, Nevada and Utah. These are all Western states, and except for Idaho, warm states.

3.20 a. Very Large Large 1 023478 2 369 8 3 0033589 99 4 0366 8711 5 012355 9730 6 2 7 8 3 9

b. The statement is not true, since there are large urban areas with extra travel time higher than very large urban areas. It is more accurate to say that “very large urban areas tend to have higher extra travel times than large urban areas.”

3.23 Wind Speed Range Frequency 25-30 6 30-35 12 35-40 13 Remember that 35.0 goes in the 35-40 group 40-45 5 45-50 2 50-55 2 55-60 1 60-65 4

I don’t have software to make proper histograms, so see the last pages for the histogram. The distribution of wind speeds is positively skewed and bimodal, with peaks around 35 m/s and 63 m/s

3.26 Cost per Month Frequency Relative Frequency 0-3 7 .137 3-6 3 .059 6-9 15 .294 9-12 11 .216 12-15 8 .157 15-18 4 .078 18-21 3 .059

b. See last page for histogram. The data is bimodal with peaks at the 0-3 and 6-9 groupings. The data is positively skewed. c. Using the relative frequencies, we can see that (.137+.059+.294+.216+(1/3)(.157)), or roughly 76% of the states have costs below $13/month.

3.28 a. Unequal widths were used to show detail in the data at low numbers. If these narrow widths were used throughout, there would be 24 divisions, which is too many to deal with easily. b. Commute Frequency Relative Frequency Density Cumulative Time Density (d) 0 to <5 5200 =5200/100400=.052 =.052/5=.0104 .052 5 to <10 18200 .181 .0363 .233 10 to <15 19600 .195 .0390 .428 15 to <20 15400 .153 .0307 .581 20 to <25 13800 .137 .0275 .718 25 to <30 5700 .057 .0114 .775 30 to <35 10200 .102 .0203 .877 35 to <40 2000 .020 .0040 .897 40 to <45 2000 .020 .0040 .917 45 to <60 4000 .040 =.040/15=.0027 .957 60 to <90 2100 .021 .0007 .978 90 to <120 2200 .022 .0007 1 c. See last page. (I messed up my bars. The horizontal lines sticking out to the left of each shouldn’t be there) The vast majority of commute times are between 5 and 35 minutes. The distribution is positively skewed and unimodal, but with a trough at 25-30 minutes. d.

e. i. Approx. .9 ii. Approx 1-.65=.35 iii. Approx 18 minutes

3.30 a. The distribution might be unimodal and negatively skewed (more scores at higher levels) b. The distribution would probably still be negatively skewed but with a peak much lower than in (a). There might be two peaks, one around 70% and another smaller one in the 90s, since some people might still do well. c. It is likely that there would be a bimodal distribution.

3.31 Number of attempts Frequency Relative Frequency Density 0 778 =778/1817=.428 .428/1=.428 1 306 .168 .168 2 274 .151 .151 3-4 221 .122 =.122/2=.0608 5-10 238 .131 =.131/5=.0261

See last page for histogram

The data shows a constantly increasing rate of homes with only a wireless phone. The rate is fairly steady, but the fall (June-Dec) seems to increase more than spring (Dec-June).

3.40 a. The scatterplot does not strongly support the statement that more expensive helmets receive higher ratings. The highest rated helmet is near the middle the cost range, and the lowest rated helmet is not the cheapest one. A $20 helmet was rated higher than a $50 helmet. But there is a very weak overall correlation. 3.41 There is a weak negative relationship between shoe cost and quality b.

The mens options have a larger range of both price and quality. There is a weak negative correlation between cost and quality. Women’s shoes tend to be higher quality, but cost does not seem to correlate to quality.

3.42 The graph shows an increase in overdose deaths over time, but not at a constant rate. The early 2000s had a very large increase.

3.45 There seem to be seasonal peaks at week 3, weeks 6-8 and week 14. There are seasonal lows at week 2, week 6, and week 18.