# Find the median and 5 number summary by hand, statistics homework help

Unit 1 Lesson 6 Assignmen

1) On the first day of finals 20 students at La Platta College were randomly selected. They were asked how many hours they had slept the night before. The results, in hours, were

8 6 5 6 4 3 5 8 7 7 5 6 2 0 5 7 6 6 7 8

Find the median and 5 number summary by hand . Show all of your work for full credit. Draw a box plot as well.

Min = ______ Q1 = _______ Med. = _______ Q3 = ________ Max = ______

2) A survey was mad to determine the number of hamburgers sold by McFarland hamburger stands during August in the Denver metropolitan area. For each of the seven McFarland stands, the number of hamburgers (in thousands) is as follows:

18 7 5 9 12 5 6

Make a stemplot of the data. Which measure of CENTER should you used based on your stemplot? Why? Find center of the data with the measure you chose.

3) Last year a small accounting firm paid each of its five clerks \$22,000, 2 junior accountants \$50,000 each, and the firm’s owner \$270,000. What is the mean salary paid at this firm? How many employees earn less than that mean? What is the median salary?

4) A news article reports that of the 411 players on National Basketball Association rosters in February 1998, only 139 “made more than the league average salary” of \$2.36 million. Is \$2.36 million the mean or median salary for NBA players? How do you know?

.5) Find the 5 Number summaries for Predators and Non-predators using the given stem plots. Draw both boxplots and then write a few sentences comparing the two distributions.

Display 2.48 shows a back-to-back stemplot for the average life spans of predators and nonpredators.              Predators                     Nonpredators

1                  0               34

75                0             556788

22222           1              0002222

65               1                555555

2                0000

5                 2

3                    5

4                     1

1    5 stands for 15 years non-predators

6    1 stands for 16 years predators

6) How much do users pay for Internet access? Here are the monthly fees (in dollars) paid by a random sample of 50 users of commercial Internet service providers in August 2000

: 9  20  40  22  22  21  21  20  10  20  20

20  13  18  50  20  18  15  8  22  25

22 10  20  22  22  21  15  23  30 12

9  20  40  22  29  19  15  20  20  20

20 15 19  21  14  22  21  35  20  22

(a) Make a stemplot of these data. Briefly describe the pattern you see. About how much do you think America Online and its larger competitors were charging in August 2000? Are there any outliers?

(b) To report a quick summary of how much people pay for Internet service, do you prefer x and s or the five-number summary? Why? Calculate your preferred summary.

7) A household’s “net worth” is the total value of the household’s possessions and investments less the total of its debts. In 2000, the mean and median net worth of American households were \$55,000 and \$182,000. Which of these numbers is the mean and which is the median? Explain your reasoning.

8) Do women study more than men? We asked the students in a large first-year college class how many minutes they studied on a typical weeknight. Here are the responses of random samples of 30 women and 30 men from the class:

Women                                                                             Men

180 120 180 360 240                                          90 120 30 90 200

120 180 120 240 170                                          90 45 30 120 75

150 120 180 180 150                                        150 120 60 240 300

200 150 180 150 180                                         240 60 120 60 30

120 60 120 180 180                                           30 230 120 95 150

90 240 180 115 120                                           0 200 120 120 180

(a) Examine the data. Why are you not surprised that most responses are multiples of 10 minutes? We eliminated one student who claimed to study 30,000 minutes per night. Are there any other responses you consider suspicious?

(b) Make a back-to-back stemplot of these data. Does it appear that women study more than men (or at least claim that they do)? Give numerical summaries that back up your conclusion.

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