The formula for Standard Deviation depends on whether you are analyzing population data, in which case it is called σ or estimating the population standard deviation from sample data, which is called s:

how to calculate standard deviationThe steps to calculating the standard deviation are:

  1. Calculate the mean of the data set (x-bar or 1. μ)
  2. Subtract the mean from each value in the data set2.
  3. Square the differences found in step 23.
  4. Add up the squared differences found in step 34.
  5. Divide the total from step 4 by either N (for population data) or (n – 1) for sample data (Note: At this point, you have the variance of the data)

Take the square root of the result from step 5 to get the standard deviation.

Example:

Step 1: The average depth of this river, x-bar, is found to be 4’.example of standard deviation

 

Step 5: The sample variance can now be calculated:example of a standard deviation chart

Step 6: To find the sample standard deviation, calculate the square root of the variance:

formula for standard deviation