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Solved: The first four deviations from the mean in a

Probability and Statistics for Engineering and the Sciences | 8th Edition | ISBN: 9780538733526 | Authors: Jay L. Devore ISBN: 9780538733526 61

Solution for problem 52E Chapter 1

Probability and Statistics for Engineering and the Sciences | 8th Edition

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Probability and Statistics for Engineering and the Sciences | 8th Edition | ISBN: 9780538733526 | Authors: Jay L. Devore

Probability and Statistics for Engineering and the Sciences | 8th Edition

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Problem 52E

Problem 52E

The first four deviations from the mean in a sample of n= 5 reaction times were .3, .9, 1.0, and 1.3. What is the fifth deviation from the mean? Give a sample for which these are the five deviations from the mean.

Step-by-Step Solution:
Step 1 of 3

Solution 52E

Step1 of 2:

From the given problem we have a sample size n = 5. And also we have 0.3, 0.9, 1.0, and 1.3.

We need to find the fifth deviation from the mean and we have to give a sample for which these are the five deviations from the mean.


Step2 of 2:

Let the sum of the deviations is:

0.3 + 0.9 + 1.0 + 1.3 = 3.5

The fifth deviation must be equal to 0 - 0.35 = -0.35.

Sample is given by:

8.3, 8.9, 9.0, 9.3, and 4.5

Then, sum of the sample deviations is:

8.3 + 8.9 + 9.0 + 9.3 + 4.5 = 40

Now, Mean of the sample deviations is:

 

   

We know that the the first four deviations are 0.3, 0.9, 1.0, 1.3, and the fifth deviation is:

Deviation = item - mean

        = 4.5 - 8

    = -3.5

 

Therefore, The fifth deviations is -3.5. And the sample is 8.3, 8.9, 9.0, 9.3, and 4.5.


  

Step 2 of 3

Chapter 1, Problem 52E is Solved
Step 3 of 3

Textbook: Probability and Statistics for Engineering and the Sciences
Edition: 8
Author: Jay L. Devore
ISBN: 9780538733526

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