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Chapter 2: Q R2.2. (page 147)

Computer use Mrs. Causey asked her students how much time they had spent

watching television during the previous week. The figure shows a cumulative relative frequency graph of her students’ responses.

a. At what percentile is a student who watched TV for 7 hours last week?

b. Estimate from the graph the interquartile range (IQR) for time spent watching TV.

Short Answer

Expert verified

Part (a) The percentile is 57

Part (b) The value is 9.00

Step by step solution

01

Part (a) Step 1: Given information

The plot is:

02

Part (a) Step 2: Concept

The percentile of an individual is the percentage of the distribution that is less than the data value of the individual.

03

Part (a) Step 3: Explanation

The student will spend 7 hours per week, according to the information provided. Construct a vertical line that cuts the x-axis at 19.50 to obtain the percentile. Create a horizontal line to connect the vertical and horizontal lines. Both lines overlap at the 57th percentile, as can be seen.

Thus, the required percentile is 57

04

Part (b) Step 1: Calculation

The third quartile and first quartile, according to the plot, are 11 and 2 respectively.

Thus, the interquartile range is:

IQR=Q3−Q1=11−2=9.00

Thus, the required value is 9.00

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