Name_____________________________________________________ Period__________

Homework 1.3

1. The 2011 roster of the Dallas Cowboys professional football team included 7 defensive linemen. Their weights (in pounds) were 321, 285, 300, 285, 286, 293, and 298.

(a) Calculate the mean. Show your work.

(b) Find the median by hand. Show your work.

(c) Suppose the heaviest lineman had weighed 341 pounds instead of 321 pounds. How would this change affect the mean and the median? What property of measures of center does this illustrate?

(d) Find and interpret the interquartile range (IQR).

(e) Determine whether there are any outliers. Show your work.

2. Here are the scores of Mrs. Lakey’s students on their first statistics test last year:

93 93 87.5 91 94.5 72 96 95 93.5 93.5 7382 45 88 80 86 85.5 87.5 81 78 86 8992 91 98 85 82.5 88 94.5 43

(a) Sketch the boxplot of the test score data. Be sure to check for outliers.

(b) Describe the distribution of Mrs. Lakey’s first test?

3. Do male doctors perform more cesarean sections (C-sections) than female doctors? A study in Switzerland examined the number of cesarean sections (surgical deliveries of babies) performed in a year by samples of male and female doctors. Here are summary statistics for the two distributions:

(a) Based on the computer output, which distribution would you guess has a more symmetrical shape? Explain.

(b) Explain how the IQRs of these two distributions can be so similar even though the standard deviations are quite different.

(c) Does it appear that male doctors perform more C-sections? Justify your answer.

4. Measuring spread Which of the distributions shown has a larger standard deviation? Justify your answer.

x sx Min Q1 Med Q3 Max IQRMale doctors 41.333 20.607 20 27 34 59 86 23Female doctors 19.1 10.126 5 10 18.5 29 33 19

Multiple choice: Select the best answer for Exercises 5 to 8.

5. If a distribution is skewed to the right with no outliers,

(a) mean < median. (b) mean > median.(c) mean ≈ median.(d) We can’t tell without examining the data.(e) mean = median.

6. The scores on a statistics test had a mean of 81 and a standard deviation of 9. One student was absent on the test day, and his score wasn’t included in the calculation. If his score of 84 was added to the distribution of scores, what would happen to the mean and standard deviation?

(a) Mean will increase, and standard deviation will increase.(b) Mean will increase, and standard deviation will decrease.(c) Mean will increase, and standard deviation will stay the same.(d) Mean will decrease, and standard deviation will increase.(e) Mean will decrease, and standard deviation will decrease.

7. The stemplot shows the number of home runs hit by each of the 30 Major League Baseball teams in 2011. Home run totals above what value should be considered outliers?

(a) 173 (b) 210 (c) 222 (d) 229 (e) 257

8. Which of the following boxplots best matches the distribution shown in the histogram?

9. Let’s chat (1.1) The bar graph displays data on students’ responses to the question “Which of these methods do you most often use to communicate with your friends?”

(a) Would it be appropriate to make a pie chart for these data? Why or why not?

(b) Jerry says that he would describe this bar graph as skewed to the right. Explain why Jerry is wrong.

10. Success in college (1.1) The 2007 Freshman Survey asked first-year college students about their “habits of mind”—specific behaviors that college faculty have identified as being important for student success. One question asked students, “How often in the past year did you revise your papers to improve your writing?” Another asked, “How often in the past year did you seek feedback on your academic work?” The figure is a bar graph comparing male and female responses to these two questions.

What does the graph tell us about the habits of mindof male and female college freshmen?