How to solve SD in plain English

Suppose you're looking to find the SD of a sample of these numbers:

1,2,2,2,3,4,9,9

If your mind works better using words over formulas, you can solve for the SD by following these steps:

1. Solve for the average (mean) of the values reported. In this case, the average is 4.

2. Find the difference between each value reported and the mean.

1- 4 = -3
2- 4= -2
2- 4= -2
2-4= -2
3- 4= -1
4- 4= 0
9- 4= 5
9- 4= 5

3. Square each of the differences (as shown below).

-3*-3 = 9
-2*-2= 4
-2*-2 = 4
-2 * -2 = 4
-1*-1 = 1
0*0 = 0
5*5 = 25
5*5 = 25


4. Sum the totals:

9+4+4+4+1+0+25+25 = 72

5. Divide by N-1

72/7 = 10.286

6. Take the square root.

The square root of 28.57 = 3.207

The SD is 3.21.