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Chapter 2: Q38. (page 94)

Parking at a university has become a problem. The university’s administrators are interested in determining the average time it takes a student to find a parking spot. An administrator inconspicuously followed 190 students and recorded how long it took each of them to find a parking spot. The durations had a distribution that was skewed to the left. Based on this information, discuss the relationship between the mean and the median for the 190 times collected.

Short Answer

Expert verified

Mean< Median

Step by step solution

01

Explaining the skewness toward left

The skewness shows the asymmetry and how distorted a variable is from the normal distribution. The variable could be skewed to the left or right.

02

Determining the relationship between mean and median

The researchers used observations to record the time it took for students to obtain the parking spot, and their findings indicate that the distribution was skewed toward the left. The relationship between mean and median is that the mean is lower than the median in this case as the distribution is skewed to the left.

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Most popular questions from this chapter

Crude oil biodegradation.Refer to the Journal of Petroleum Geology (April 2010) study of the environmental factors associated with biodegradation in crude oil reservoirs, Exercise 2.29 (p. 85). Recall that amount of dioxide (milligrams/liter) and presence/absence of crude oil were determined for each of 16 water specimens collected from a mine reservoir. The data are repeated in the accompanying table.

Dioxide Amount

Crude Oil Present

3.3

No

0.5

Yes

1.3

Yes

0.4

Yes

0.1

No

4.0

No

0.3

No

0.2

Yes

2.4

No

2.4

No

1.4

No

0.5

Yes

0.2

Yes

4.0

No

4.0

No

4.0

No

a.Find the mean dioxide level of the 16 water specimens. Interpret this value.

b.Find the median dioxide level of the 16 water specimens. Interpret this value.

c.Find the mode of the 16 dioxide levels. Interpret this value.

d.Find the median dioxide level of the 10 water specimens with no crude oil present.

e.Find the median dioxide level of the 6 water specimens with crude oil present.

f.Compare the results, parts d and e. Make a statement about the association between dioxide level and presence/absence of crude oil.

Cable TV subscriptions and “cord cutters.” Has the increasing popularity of smartphones and video streaming over the Internet affected cable and satellite TV subscriptions? This was one of the questions of interest in a recent Pew Research Center survey (December 2015). Telephone (both landline and cell phone) interviews were conducted on a representative sample of 2,001 adults living in the United States. For this sample, 1,521 adults reported that they currently receive cable or satellite TV service at home, 180 revealed that they have never subscribed to cable/satellite TV service at home, and the remainder (300 adults) admitted that they are “cord cutters,” i.e., they canceled the cable/satellite TV service. The results are summarized in the Minitab pie chart shown.

a. According to the pie chart, what proportion of the adults in the sample currently have a cable/satellite TV subscription at home? Verify the accuracy of this proportion using the survey results.

b. Now consider only the 1,821 adults in the sample that have at one time or another subscribed to cable/satellite TV service. Create a graph that compares the proportions of adults who currently subscribe to cable/satellite TV service with the proportion who are “cord cutters.”

Refer to Exercise 2.141. Assuming all populations are approximately mound-shaped, for parts a–d, determine whether the values 0, 4, and 12 are outliers.

Motivation of drug dealers.Consider a study of drug dealers and their motivation for participating in the illegal drug market (Applied Psychology in Criminal Justice, September 2009). The sample consisted of 100 convicted drug dealers who attended a court-mandated counseling program. Each dealer was scored on the Wanting Recognition (WR) Scale, which provides a quantitative measure of a person’s level of need for approval and sensitivity to social situations. (Higher scores indicate a greater need for approval.) The sample of drug dealers had a mean WR score of 39, with a standard deviation of 6. Assume the distribution of WR scores for drug dealers is mound-shaped and symmetric.

a.Give a range of WR scores that will contain about 95% of the scores in the drug dealer sample.

b.What proportion of the drug dealers had WR scores above 51?

c.Give a range of WR sores that contain nearly all the scores in the drug dealer sample.

Question: Given a data set with a largest value of 760 and a smallest value of 135, what would you estimate the standard deviation to be? Explain the logic behind the procedure you used to estimate the standard deviation. Suppose the standard deviation is reported to be 25. Is this feasible? Explain
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