3. Describing Data Numerically

Find the median of the sample data below.

Resistant Measures Listed below are 10 wait times (minutes) for “Rock ‘n’ Roller Coaster” at 10 AM (from Data Set 33 “Disney World Wait Times”). The data are listed in order from lowest to highest. Find the mean and median of these ten values. Then find the mean and median after excluding the value of 180, which appears to be an outlier. Compare the two sets of results. How much was the mean affected by the inclusion of the outlier? How much is the median affected by the inclusion of the outlier?

15 20 25 30 30 35 45 50 50 180 

Critical Thinking. For Exercises 5–20, watch out for these little buggers. Each of these exercises involves some feature that is somewhat tricky. Find the (a) mean, (b) median, (c) mode, (d) midrange, and then answer the given question.

Geography Majors The data listed below are estimated incomes (dollars) of students who graduated from the University of North Carolina (UNC) after majoring in geography. The data are based on graduates in the year 1984. The income of basketball superstar Michael Jordan (a 1984 UNC graduate and geography major) is included. Does his income have much of an effect on the measures of center? Based on these data, would the college have been justified by saying that the mean income of a graduate in their geography program is greater than \$250,000?

17,466 18,085 17,875 19,339 19,682 19,610 18,259 16,354 2,200,000

Critical Thinking. For Exercises 5–20, watch out for these little buggers. Each of these exercises involves some feature that is somewhat tricky. Find the (a) mean, (b) median, (c) mode, (d) midrange, and then answer the given question.

Smart Thermostats Listed below are selling prices (dollars) of smart thermostats tested by Consumer Reports magazine. If you decide to buy one of these smart thermostats, what statistic is most relevant, other than the measures of central tendency?

250 170 225 100 250 250 130 200 150 250 170 200 180 250

Critical Thinking. For Exercises 5–20, watch out for these little buggers. Each of these exercises involves some feature that is somewhat tricky. Find the (a) mean, (b) median, (c) mode, (d) midrange, and then answer the given question.

Caffeine in Soft Drinks Listed below are measured amounts of caffeine (mg per 12 oz of drink) obtained in one can from each of 20 brands (7-UP, A&W Root Beer, Cherry Coke, . . . , Tab). Are the statistics representative of the population of all cans of the same 20 brands consumed by Americans?

0 0 34 34 34 45 41 51 55 36 47 41 0 0 53 54 38 0 41 47

In Exercises 21–24, find the mean and median for each of the two samples, then compare the two sets of results.

Blood Pressure A sample of blood pressure measurements is taken from Data Set 1 “Body Data” in Appendix B, and those values (mm Hg) are listed below. The values are matched so that 10 subjects each have systolic and diastolic measurements. (Systolic is a measure of the force of blood being pushed through arteries, but diastolic is a measure of blood pressure when the heart is at rest between beats.) Are the measures of center the best statistics to use with these data? What else might be better?

Systolic: 118 128 158 96 156 122 116 136 126 120

Diastolic: 80  76  74  52  90  88  58   64  72  82

Large Data Sets from Appendix B. In Exercises 25–28, refer to the indicated data set in Appendix B. Use software or a calculator to find the means and medians.

Weights Use the weights of the males listed in Data Set 2 “ANSUR I 1988,” which were measured in 1988 and use the weights of the males listed in Data Set 3 “ANSUR II 2012,” which were measured in 2012. Does it appear that males have become heavier?

In Exercises 21–24, find the mean and median for each of the two samples, then compare the two sets of results.

It’s a Small Wait After All Listed below are the wait times (minutes) at 10 AM for the rides “It’s a Small World” and “Avatar Flight of Passage.” These data are found in Data Set 33 “Disney World Wait Times.” Does a comparison between the means and medians reveal that there is a difference between the two sets of data?

Large Data Sets from Appendix B. In Exercises 25–28, refer to the indicated data set in Appendix B. Use software or a calculator to find the means and medians.

Body Temperatures Refer to Data Set 5 “Body Temperatures” in Appendix B and use the body temperatures for 12:00 AM on day 2. Do the results support or contradict the common belief that the mean body temperature is 98.6oF?

Planets The planets of the solar system have the numbers of moons listed below in order from the sun. (Pluto is not included because it was uninvited from the solar system party in 2006.) Include appropriate units whenever relevant.

0 0 1 2 17 28 21 8

a. Find the mean.

b. Find the median.

In Exercises 1 and 2, use the following wait times (minutes) at 10:00 AM for the Tower of Terror ride at Disney World (from Data Set 33 “Disney World Wait Times” in Appendix B).

35 35 20 50 95 75 45 50 30 35 30 30 

b. Find the median.

Nicotine in Cigarettes Some of the nonparametric methods in this chapter use ranks of data. Find the ranks corresponding to the following amounts (milligrams) of nicotine in king-sized cigarettes (from Data Set 16 “Cigarette Contents” in Appendix B).

1.1 1.7 1.7 1.1 1.4 1.0 1.2 1.8 1.6 1.1

Reported and Measured Heights Listed below are self-reported heights of males aged 16 and over and their corresponding measured heights (based on data from the National Health and Nutrition Examination Survey). All heights are in inches. First find the differences (reported height–measured height), and then use those differences to find the (a) mean, (b) median, (c) mode,

Reported and Measured Heights Listed below are self-reported heights of males aged 16 and over and their corresponding measured heights (based on data from the National Health and Nutrition Examination Survey). All heights are in inches. First find the differences (reported height–measured height), and then use those differences to find the (h) Q1, (i) Q3

Building Basic Skills and Vocabulary

True or False? In Exercises 1–4, determine whether the statement is true or false. If it is false, rewrite it as a true statement.

A data set can have the same mean, median, and mode.