Question

Consider the following sample data. Sample A: 4, 6, 8 Sample B: 63, 65, 67 Sample C: 1,010; 1,012; 1,014 (a) Find the mean and standard deviation for each sample. Sample A: Sample B: Sample C: Mean 6 6 Correct 65 65 Correct 1,002 1,002 Incorrect Sample Standard Deviation 3 3 Incorrect 3 3 Incorrect 3 3 Incorrect (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

FORMULAS USED:

SAMPLE MEAN:

SAMPLE STANDARD DEVIATION:

(a) MEAN AND STANDARD DEVIATION FOR GIVEN THREE SAMPLES:

SAMPLE A:

Sample mean

Sample standard deviation

4	-2	4
6	0	0
8	2	4

  

SAMPLE B:

Sample mean

Sample standard deviation

63	-2	4
65	0	0
67	2	4

  

SAMPLE C:

Sample mean

Sample standard deviation

1010	-2	4
1012	0	0
1014	2	4

  

(b) STANDARD DEVIATION:

Standard deviation measures the spread of a data distribution and is a function of the value of the mean. Since the standard deviation (2) is close to 0 indicates that the data points tend to be close to the mean. And the variability of data points around the mean is same for all three samples.