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Chapter 2: Q108E (page 125)

Consider the horizontal box plot shown below.


a.What is the median of the data set (approximately)?

b.What are the upper and lower quartiles of the data set (approximately)?

c.What is the interquartile range of the data set (approximately)?

d.Is the data set skewed to the left, skewed to the right, or symmetric?

e.What percentage of the measurements in the data set lie to the right of the median? To the left of the upper quartile?

f.Identify any outliers in the data.

Short Answer

Expert verified

(a) 4

(b) 6, 3

(c) 3

(d) Skewed to the right

(e) 50%, 75%

(f) 12, 13, 16

Step by step solution

01

Identifying the median

The median here is approximately 4.

02

Finding the upper and lower quartiles

Upper Quartile (QU) = 6

Lower Quartile (QL) = 3

03

Calculating the the interquartile range(IQR)

IQR = QU - QL

= 6 – 3

= 3

The interquartile range is 3.

04

Determining the skewness

The box plot is skewed to the rightbecause the right whisker is longer than the left.

05

Computing the percentage of the measurements the right of the median and to the left of the upper quartile

Median is the centermost value of the dataset. Therefore, there will be 50% measurements to the right of the median.

The upper quartile is the 75th percentile. Therefore, there are 75% of measurements to the left of the upper quartile.

06

Finding the outliers

The threeoutliers are 12, 13, and 16.

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Most popular questions from this chapter

Products “Made in the USA.”“Made in the USA” is a claim stated in many product advertisements or on product labels. Advertisers want consumers to believe that the product is manufactured with 100% U.S. labor and materials—which is often not the case. What does “Made in the USA” mean to the typical consumer? To answer this question, a group of marketing professors conducted an experiment at a shopping mall (Journal of Global Business, spring 2002). They asked every fourth adult entrant to the mall to participate in the study. A total of 106 shoppers agreed to answer the question, “‘Made in the USA’ means what percentage of U.S. labor and materials?” The responses of the 106 shoppers are summarized as follows: “100%” (64 shoppers), “75 to 99%” (20 shoppers), “50 to 74%” (18 shoppers), and “less than 50%” (4 shoppers).

a.What type of data-collection method was used?

b.What type of variable, quantitative or qualitative, is measured?

c.Present the data in graphical form. Use the graph to make a statement about the percentage of consumers who believe “Made in the USA” means 100% U.S. labor and materials.

Calculate the mode, mean, and median of the following data:

18 10 15 13 17 15 12 15 18 16 11

Permeability of sandstone during weathering.Refer to the Geographical Analysis(Vol. 42, 2010) study of the decay properties of sandstone when exposed to the weather, Exercises 2.47 and 2.65 (pp. 96 and 104). Recall that slices of sandstone blocks were measured for permeability under three conditions: no exposure to any type of weathering (A), repeatedly sprayed with a 10% salt solution (B), and soaked in a 10% salt solution and dried (C).

a.Combine the mean (from Exercise 2.47) and standard deviation (from Exercise 2.65) to make a statement about where most of the permeability measurements for Group A sandstone slices will fall. Which rule did you use to make this inference and why?

b.Repeat part afor Group B sandstone slices.

c.Repeat part afor Group C sandstone slices.

d.Based on all your analyses, which type of weathering (type A, B, or C) appears to result in faster decay (i.e., higher permeability measurements)?

U.S. business bankruptcies.The American Bankruptcy Institute and the National Bankruptcy Research Center monitor the number of business bankruptcy filings each quarter. The table below lists the number of business bankruptcy filings for each quarter of a recent 2-year period. FILING

a.Explain why the data in the table represent time series data.

b.Construct a time series plot for the quarterly number of bankruptcy filings.

c.Do you detect a trend in the time series plot? Explain.

Year

Quarter

Number of

Bankruptcies

2011

1

2

3

4

12,376

12,304

11,705

11,149

2012

1

2

3

4

10,998

10,374

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Crash tests on new cars.The National Highway Traffic Safety Administration (NHTSA) crash-tests new car models to determine how well they protect the driver and front-seat passenger in a head-on collision. The NHTSA has developed a “star” scoring system for the frontal crash test, with results ranging from one star (*) to five stars (*****). The more stars in the rating, the better the level of crash protection in a head-on collision. The NHTSA crashtest results for 98 cars (in a recent model year) are stored in the accompanying data file.

a. The driver-side star ratings for the 98 cars are summarized in the Minitab printout shown below. Use the information in the printout to form a pie chart. Interpret the graph.

Tally for Discrete Variables: DRIVSTAR

DRIVSTAR

Count

Percent

2

3

4

5

N =

4

17

59

18

98

4.08

17.35

60.20

18.37


b. One quantitative variable recorded by the NHTSA is the driver’s severity of head injury (measured on a scale from 0 to 1,500). The mean and standard deviation for the 98 driver head-injury ratings are displayed in the Minitab printout below. Give a practical interpretation of the mean.
Descriptive Statistics: DRIVHEAD

Variable

N

Mean

StDev

Minimum

Q1

Median

Q3

Maximum

DRIVHEAD

98

603.7

185.4

216.0

475.0

605.0

724.3

1240.0

C. Use the mean and standard deviation to make a statement about where most of the head-injury ratings fall.

d..Find the z-score for a driver head-injury rating of 408. Interpret the result.
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