Question

Find the SS, the variance, and the Standard Deviation of Sample A

Please be sure to show your entire work. For each step.

Sample A

8

10

18

1

6

11

9

10

10

7

Answer 1

We know, Sum of Squares (SS) = , where, is each value and is the mean of the data.

We know, Variance = = SS/(n-1)

Thus, Variance = SS/(n-1).

And, Standard Deviation = √(Variance)

The values of Sample A are : 8, 10, 18, 1, 6, 11, 9, 10, 10, 7.

We know, Mean = (Sum of all values)/(Total number of values).

Here, total number of values = 10.

Thus, Mean, = (8+10+18+1+6+11+9+10+10+7)/10 = 90/10 = 9

Thus, = 9.

Thus, SS = = = 1 + 1 + 81 + 64 + 9 + 4 + 0 + 1 + 1 + 4 = 166.

Thus, Sum of Squares, SS = 166.

Now, Variance = SS/(n-1). Here, n = 10. Thus, (n - 1) = (10 - 1) = 9.

Thus, Variance = 166/9 = 18.444(rounded up to three decimal places).

Thus, Variance = 18.444.

Now, Standard Deviation = √(Variance) = √(18.444) = 4.295(rounded up to three decimal places).

Thus, Standard Deviation = 4.295.