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.

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.