Example: Find the standard deviation for the data: 20, 23, 25, 26, 26, 23, 25, 25
The data can be grouped as follows:
f  Data 
1  20 
2  23 
3  25 
2  26 
 The arithmetic mean of the data (1*20+2*23+3*25+2*26)/8 = 24.125
The deviations from the mean are respectively:
24.125  20 = 4.125
24.125  23 = 1.125
25  24.125 = 0.875
26  24.125 = 1.875
The squares of these deviations are:
4.125^{2} = 17.015625
1.125^{2} = 1.265625
0.875^{2} = 0.765625
1.875^{2} = 3.515625
 The sum of the squared results from step 1 are now multiplied by their associated f. This gives us:
for 20, 1 * 17.015625 = 17.015625
for 23, 2 * 1.265625 = 2.53125
for 25, 3 * 0.765625 = 2.296875
for 26, 2 * 3.515625 = 7.03125
 The sum of the resulting products is 17.015625 + 2.53125 + 2.296875 + 7.03125 = 28.875.
Now divided by (n1), which is 7
28.875/7 = 4.125
 The square root of 4.125 is approximately 2.031
Answer: The Standard Deviation of the set of numbers {20, 23, 25, 26, 26, 23, 25, 25} is 2.031
Directions: Answer the following question. Also write an example of your own and try working out the standard deviation of the data.
