In this problem, we explore the effect on the standard deviation of adding the same constant to each data value in a data set. Consider the following data set.8,7,14,12,11a) use the defining formula,the computation formula,or a calculator to compute s(enter your answer to one decimal place. b)Add 8 to each data value to get to the new data set 16,15,22,20,19. Compute s(Enter your answer to one decimal place.)c) Compare the results of part(a) (b). In general, how do you think the standard deviation of a data set changes if the same constant is added to each data set value?

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Asked Nov 12, 2019
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In this problem, we explore the effect on the standard deviation of adding the same constant to each data value in a data set. Consider the following data set.

8,7,14,12,11

a) use the defining formula,the computation formula,or a calculator to compute s(enter your answer to one decimal place.

 

b)Add 8 to each data value to get to the new data set 16,15,22,20,19. Compute s(Enter your answer to one decimal place.)

c) Compare the results of part(a) (b). In general, how do you think the standard deviation of a data set changes if the same constant is added to each data set value?

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Expert Answer

Step 1

(a)

Consider, X= 8,7,14,12,11

The formula to calculate the sample standard deviation (s) is:

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(x-X) п-1

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Step 2

Here, n = 5

To calculate the sample standard deviation, sample mean is required which can be calculated as:

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ΣΧ X = 8+7 14 12+11 52 5 10.4

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Step 3

Now, the sample standard deviat...

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(8-10.4) +(7-10.4) +...+(11-10.4) 5 1 - 2.880 2.9

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