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:

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

Take the square root of the result from step 5 to get the standard deviation6.

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