To calculate the standard deviation, take the square root of the variance. Find the variance by calculating the average of the squared differences from the average of the set.
- Find the average value of the data set
To find the average value, add up all the data points in the set, and then divide by the number of data points. For example, in a data set of 4, 6, 7, 1 and 12, add up all five data points to find the sum of 30, then divide by 5 to find the average value of 6.
- Calculate the squared differences
To calculate the squared differences, subtract each number in the data set from the average value, and square it. In the example data set from Step 1, the first squared difference is (6-4)^2=4. The second squared difference is (6-6)^2=0. Find a squared difference for each data point in the data set.
- Find the variance
Find the variance by calculating the average of all the squared differences you found in Step 2. To do this, add up all the squared differences, and then divide the sum by the number of values in the set. In the example, the squared differences are 4, 0, 1, 25 and 36. The average of the squared differences is the sum of the values (66) divided by the number of data points (5). Therefore, 13.2 is the variance.
- Take the square root of the variance
Find the standard deviation by taking the square root of the variance. In the example, 13.2 is the variance, so the standard deviation is the square root of 13.2, which is 3.6.