Answer
For example, suppose the final exam scores of a sample of four students are 79, 81, 77 and 83. The mean score for these four students is :
( 79+ 81+ 77+ 83 ) / 4 = 80
The deviations of the four scores from the mean =
1) 79 - 80 = -1
2) 81 - 80 = 1
3) 77 - 80 = -3
4) 83 - 80 = 3
The sum of the deviations of the x values from the mean = -1 + 1 + (-3) + 3 = 0
As we can see above, the sum of the deviations of the x values from the mean is zero.
Therefore, the standard deviation is zero.
Work Step by Step
For example, suppose the final exam scores of a sample of four students are 79, 81, 77 and 83. The mean score for these four students is :
( 79+ 81+ 77+ 83 ) / 4 = 80
The deviations of the four scores from the mean =
1) 79 - 80 = -1
2) 81 - 80 = 1
3) 77 - 80 = -3
4) 83 - 80 = 3
The sum of the deviations of the x values from the mean = -1 + 1 + (-3) + 3 = 0
As we can see above, the sum of the deviations of the x values from the mean is zero.
Therefore, the standard deviation is zero.
