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

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80

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100

6.97

125

7.39

150

7.61

200

7.78

250

7.92

300

8.20

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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

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Job Status

Wave 1

Wave 4

Working, No MBA

2,657

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Working, Have MBA

0

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Not Working, Business School

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Not Working, Other
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Network Type/
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Number of
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WLAN / Single

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WSN / Single

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AHN / Single

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WLAN / Multi

14

WSN / Multi

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AHN / Multi

5

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Percent

2

3

4

5

N =

4

17

59

18

98

4.08

17.35

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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

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216.0

475.0

605.0

724.3

1240.0

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

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