Question

You want to find the standard deviation of the musical aptitude scores for a group of pre-schoolers. Scores range from 0 to 10. Here are the scores of the eight children in the group:

3   9   8   9   0   9   7   3

Find the mean of this data set:

Now, use the mean to find the deviation for each score. The deviation is the score minus the mean.

Data Value	Deviation = Data Value - Mean
3
9
8
9
0
9
7
3

What is the sum of all the deviations?

Answer 1

Solution :

x	Deviation = x -	(x - )2
3	-3	9
9	3	9
8	2	4
9	3	9
0	-6	36
9	3	9
7	1	1
3	-3	9
x = 48	(x - ) = 0	(x - )2 = 86

The sum of all the deviations = 0

Mean = x / n = 48 / 8 = 6

=  (x - )² / n = 86 / 8 = 3.2787

Standard deviation = 3.2787