Question

Consider the following sample data.

Sample A:	9, 15, 21
Sample B:	67, 73, 79
Sample C:	1,030; 1,036; 1,042

(a) Find the mean and standard deviation for each sample.

	Sample A:	Sample B:	Sample C:
Mean
Sample Standard Deviation

(b) What does this exercise show about the standard deviation?

• The idea is to illustrate that the standard deviation is not a function of the value of the mean.

• The idea is to illustrate that the standard deviation is a function of the value of the mean.

Answer 1

We know for a sample we have

Sample mean and

Sample standard deviation

a) Using these formulas we see that

	Sample A:	Sample B:	Sample C:
Mean	15	73	1036
Sample Standard Deviation	6	6	6

b) The above exercise shows that the standard deviation is not a function of the value of the mean

As mean were different for the three samples but the standard deviation remained the same .