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:
The 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, you have the variance of the data)
Take the square root of the result from step 5 to get the standard deviation.
Step 1: The average depth of this river, x-bar, is found to be 4’.
Step 6: To find the sample standard deviation, calculate the square root of the variance: