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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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Most popular questions from this chapter

How does the speed of a runner vary over the course of a marathon (a distance of 42.195 km)? Consider determining both the time to run the first 5 km and the time to run between the 35-km and 40-km points, and then subtracting the former time from the latter time. A positive value of this difference corresponds to a runner slowing down toward the end of the race. The accompanying histogram is based on times of runners who participated in several different Japanese marathons (鈥淔actors Affecting Runners鈥� Marathon Performance,鈥� Chance, Fall, 1993: 24鈥�30).What are some interesting features of this histogram? What is a typical difference value? Roughly what proportion of the runners ran the late distance more quickly than the early distance?

Consider the population consisting of all computers of acertain brand and model, and focus on whether a computerneeds service while under warranty.

a. Pose several probability questions based on selecting a sample of 100 such computers.

b. What inferential statistics question might be answeredby determining the number of such computers in a sample of size 100 that need warranty service?

A sample of 77 individuals working at a particular office wasselected and the noise level (dBA) experienced by each individual was determined, yielding the followingdata (鈥淎cceptable Noise Levels for Construction Site Offices,鈥� Building Serv. Engr. Research and Technology, 2009: 87鈥�94).

55.3

55.3

55.3

55.9

55.9

55.9

55.9

56.1

56.1

56.1

56.1

56.1

56.1

56.8

56.8

57.0

57.0

57.0

57.8

57.8

57.8

57.9

57.9

57.9

58.8

58.8

58.8

59.8

59.8

59.8

62.2

62.2

63.8

63.8

63.8

63.9

63.9

63.9

64.7

64.7

64.7

65.1

65.1

65.1

65.3

65.3

65.3

65.3

67.4

67.4

67.4

67.4

68.7

68.7

68.7

68.7

69.0

70.4

70.4

71.2

71.2

71.2

73.0

73.0

73.1

73.1

74.6

74.6

74.6

74.6

79.3

79.3

79.3

79.3

83.0

83.0

83.0

Use various techniques discussed in this chapter to organize, summarize, and describe the data.

Let \({{\rm{X}}_{\rm{1}}}{\rm{,}}{{\rm{X}}_{\rm{2}}}.....{\rm{,}}{{\rm{X}}_{\rm{n}}}\) represent a random sample from the Rayleigh distribution with density function given in Exercise \({\rm{15}}\). Determine a. The maximum likelihood estimator of \({\rm{\theta }}\), and then calculate the estimate for the vibratory stress data given in that exercise. Is this estimator the same as the unbiased estimator suggested in Exercise \({\rm{15}}\)? b. The mle of the median of the vibratory stress distribution. (Hint: First express the median in terms of \({\rm{\theta }}\).)

A sample of 20 glass bottles of a particular type was selected, and the internal pressure strength of each bottle was determined. Consider the following partial sample information:
median = 202.2 lower fourth = 196.0
upper fourth = 216.8

Three smallest observations 125.8 188.1 193.7
Three largest observations 221.3 230.5 250.2


a. Are there any outliers in the sample? Any extreme outliers?
b. Construct a boxplot that shows outliers, and comment on any interesting features.
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