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Chapter 1: Q31E (page 29)

The cumulative frequency and cumulative relativefrequency for a particular class interval are the sum offrequencies and relativefrequencies, respectively, forthat interval and all intervals lying below it. If, forexample, there are four intervals with frequencies 9,16, 13, and 12, then the cumulative frequencies are 9,25, 38, and 50, and the cumulative relative frequenciesare .18, .50, .76, and 1.00. Compute the cumulativefrequencies and cumulative relative frequencies for thedata of Exercise 24.

Short Answer

Expert verified

The cumulative frequency and the cumulative relative frequency is,

x

Cumulative frequency

Cumulative Relative Frequency

4000-4200

1

0.01

4200-4400

3

0.03

4400-4600

12

0.12

4600-4800

24

0.24

4800-5000

43

0.43

5000-5200

65

0.65

5200-5400

85

0.85

5400-5600

92

0.92

5600-5800

99

0.99

5800-6000

100

1

Step by step solution

01

Given information

The cumulative frequency and cumulative relative frequency for a particular class interval are the sum of frequencies and relative frequencies, respectively, for that interval and all intervals lying below it.

02

Compute the cumulative frequencies and cumulative relative frequencies

Referring to the exercise 24, we have,

x representing the shear strength (lb) of ultrasonic spot welds.

The table representing the frequency and relative frequency as,

x

Frequency

Relative Frequency

4000-4200

1

0.01

4200-4400

2

0.02

4400-4600

9

0.09

4600-4800

12

0.12

4800-5000

19

0.19

5000-5200

22

0.22

5200-5400

20

0.2

5400-5600

7

0.07

5600-5800

7

0.07

5800-6000

1

0.01

Using the given information, the cumulative frequency and the cumulative relative frequency is represented as,

x

Cumulative frequency

Cumulative Relative Frequency

4000-4200

1

0.01

4200-4400

3

0.03

4400-4600

12

0.12

4600-4800

24

0.24

4800-5000

43

0.43

5000-5200

65

0.65

5200-5400

85

0.85

5400-5600

92

0.92

5600-5800

99

0.99

5800-6000

100

1

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