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Each of 16 students measured the circumference of a tennis

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 12E Chapter 1.2

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

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Problem 12E

Each of 16 students measured the circumference of a tennis ball by four different methods, which were:

Method A: Estimate the circumference by eye.

Method B: Measure the diameter with a ruler, and then compute the circumference.

Method C: Measure the circumference with a ruler and string.

Method D: Measure the circumference by rolling the ball along a ruler.

The results (in cm) are as follows, in increasing order for each method:

Method A: 18.0, 18.0, 18.0, 20.0, 22.0, 22.0, 22.5,

23.0, 24.0, 24.0, 25.0, 25.0, 25.0, 25.0, 26.0, 26.4.

Method B: 18.8, 18.9, 18.9, 19.6, 20.1, 20.4, 20.4,

20.4, 20.4, 20.5, 21.2, 22.0, 22.0, 22.0, 22.0, 23.6.

Method C: 20.2, 20.5, 20.5, 20.7, 20.8, 20.9, 21.0,

21.0, 21.0, 21.0, 21.0, 21.5, 21.5, 21.5, 21.5, 21.6.

Method D: 20.0, 20.0, 20.0, 20.0, 20.2, 20.5, 20.5,

20.7, 20.7, 20.7, 21.0, 21.1, 21.5, 21.6, 22.1, 22.3.

a. Compute the mean measurement for each method.

b. Compute the median measurement for each method.

c. Compute the 20% trimmed mean measurement for each method.

d. Compute the first and third quartiles for each method.

e. Compute the standard deviation of the measurements for each method.

f. For which method is the standard deviation the largest? Why should one expect this method to have the largest standard deviation?

g. Other things being equal, is it better for a measurement method to have a smaller standard deviation or a larger standard deviation? Or doesn’t it matter? Explain.

Step-by-Step Solution:

Answer :

Step 1 of 7 :

Given a tennis ball by by four different method.

Each of 16 student measured.

Here n=16

Our goal is to find

a). Compute the mean measurement for each method.

b). Compute the median measurement for each method.

c). Compute 20% trimmed mean measurement for each method.

d). Compute the first and third quartile for each method.

e). The standard deviation of the measurement for each method.

f). For which method is the standard deviation the largest ?Why should one except this have  

     method to have the largest standard deviation.

g). Other things being equal,is it better for a measurement method to have a smaller standard deviation or a larger standard deviation ?or doesn’t it matter? Explain.

Step 1 of 7 :

a).

Now we have to compute the mean measurement for each method.

Method A :

18

24

18

24

18

25

20

25

22

25

22

25

22.5

26

23

26.4

Now we have to find the mean of method A.

Mean is the sum of the total numbers in the data set and divided by the total number.

Then the formula of the mean is

                                   

                                   

                                 

Therefore the method A mean is

Method B :

18.8

20.4

18.9

20.5

18.9

21.2

19.6

22

20.1

22

20.4

22

20.4

22

20.4

23.6

Now we have to find the mean of method B.

Mean is the sum of the total numbers in the data set and divided by the total number.

Then the formula of the mean is

                                   

                                   

                                 

Therefore the method B mean is

Method C :

20.2

21.0

20.5

21.0

20.5

21.0

20.7

21.5

20.8

21.5

20.9

21.5

21.0

21.5

21.0

21.6

Now we have to find the mean of method C.

Mean is the sum of the total numbers in the data set and divided by the total number.

Then the formula of the mean is

                                   

                                   

                                 

Therefore the method C mean is

Method D :

20

20.7

20

20.7

20

21

20

21.1

20.2

21.5

20.5

21.6

Step 2 of 1

Chapter 1.2, Problem 12E is Solved
Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. Since the solution to 12E from 1.2 chapter was answered, more than 1460 students have viewed the full step-by-step answer. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. The full step-by-step solution to problem: 12E from chapter: 1.2 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. The answer to “?Each of 16 students measured the circumference of a tennis ball by four different methods, which were:Method A: Estimate the circumference by eye.Method B: Measure the diameter with a ruler, and then compute the circumference.Method C: Measure the circumference with a ruler and string.Method D: Measure the circumference by rolling the ball along a ruler.The results (in cm) are as follows, in increasing order for each method:Method A: 18.0, 18.0, 18.0, 20.0, 22.0, 22.0, 22.5,23.0, 24.0, 24.0, 25.0, 25.0, 25.0, 25.0, 26.0, 26.4.Method B: 18.8, 18.9, 18.9, 19.6, 20.1, 20.4, 20.4,20.4, 20.4, 20.5, 21.2, 22.0, 22.0, 22.0, 22.0, 23.6.Method C: 20.2, 20.5, 20.5, 20.7, 20.8, 20.9, 21.0,21.0, 21.0, 21.0, 21.0, 21.5, 21.5, 21.5, 21.5, 21.6.Method D: 20.0, 20.0, 20.0, 20.0, 20.2, 20.5, 20.5,20.7, 20.7, 20.7, 21.0, 21.1, 21.5, 21.6, 22.1, 22.3.a. Compute the mean measurement for each method.b. Compute the median measurement for each method.c. Compute the 20% trimmed mean measurement for each method.d. Compute the first and third quartiles for each method.e. Compute the standard deviation of the measurements for each method.f. For which method is the standard deviation the largest? Why should one expect this method to have the largest standard deviation?g. Other things being equal, is it better for a measurement method to have a smaller standard deviation or a larger standard deviation? Or doesn’t it matter? Explain.” is broken down into a number of easy to follow steps, and 221 words. This full solution covers the following key subjects: method, compute, standard, deviation, Circumference. This expansive textbook survival guide covers 153 chapters, and 2440 solutions.

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Each of 16 students measured the circumference of a tennis