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Chapter 2: Q107E (page 125)

Suppose a data set consisting of exam scores has a lower quartile QL = 60, a median QM = 75, and an upper quartile QU = 85. The scores on the exam range from 18 to 100. Without having the actual scores available to you, construct as much of the box plot as possible.

Short Answer

Expert verified

IQR = QU – QL

= 85 – 60

= 25

Lower Inner Fence = QL - 1.5(IQR)

= 60 – 1.5(25)

= 60 – 37.5

= 22.5

Upper Inner Fence = QU + 1.5(IQR)

= 60 + 1.5(25)

= 60 + 37.5

= 122.5

Step by step solution

01

Finding the fences

IQR = QU – QL

= 85 – 60

= 25

Lower Inner Fence = QL - 1.5(IQR)

= 60 – 1.5(25)

= 60 – 37.5

= 22.5

Upper Inner Fence = QU + 1.5(IQR)

= 60 + 1.5(25)

= 60 + 37.5

= 122.5

02

Creating the box plot

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Most popular questions from this chapter

Question: Repair and replacement costs of water pipes.Pipes used in a water distribution network are susceptible to breakage due to a variety of factors. When pipes break, engineers must decide whether to repair or replace the broken pipe.

A team of civil engineers estimated the ratio of repair to replacement cost of commercial pipe based on the diameter (in millimeters) of the pipe. (IHS Journal of Hydraulic Engineering,September 2012.) Data for a sample of 13 different pipe sizes are provided in the table. Use a scatterplot to aid the engineers in detecting a trend in the data. Does it appear that the ratio of repair to replacement cost is strongly associated with pipe size?

DIAMETER

RATIO

80

6.58

100

6.97

125

7.39

150

7.61

200

7.78

250

7.92

300

8.20

350

8.42

400

8.60

450

8.97

500

9.31

600

9.47

700

9.72

Give the percentage of measurements in a data set that are above and below each of the following percentiles:

a. 75th percentile

b. 50th percentile

c. 20th percentile

d. 84th percentile

The economic return to earning an MBA. Refer to the International Economic Review (August 2008) study on the economic rewards to obtaining an MBA degree, Exercise 1.27 (p. 51). Job status information was collected for a sample of 3,244 individuals who sat for the GMAT in each of four time periods (waves). Summary information (number of individuals) for Wave 1 (at the time of taking the GMAT) and Wave 4 (7 years later) is provided in the accompanying table. Use a graph to compare and contrast the job status distributions of GMAT takers in Wave 1 and Wave 4.

Job Status

Wave 1

Wave 4

Working, No MBA

2,657

1,787

Working, Have MBA

0

1,372

Not Working, Business School

0

7

Not Working, Other
Graduate School

36

78

Not Working, 4-Year
Institution

551

0

Total

3,244

3,244

Jamming attacks on wireless networks. Refer to the International Journal of Production Economics (Vol. 172, 2016) study of U.S. military jamming attacks on wireless networks used by terrorists, Exercise 1.16 (p. 50). Recall that 80 recent jamming attacks were classified according to network type (WLAN, WSN, or AHN) attacked and number of channels (single- or multi-channel) of the network. The results are summarized in the accompanying table.

Network Type/
Number of Channels

Number of
Jamming Attacks

WLAN / Single

31

WSN / Single

13

AHN / Single

8

WLAN / Multi

14

WSN / Multi

9

AHN / Multi

5

Total

80

a. Construct a Pareto diagram for the data. Interpret the results.

b. Construct a pie chart for network type only. Interpret the results.

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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