How to Calculate Standard Deviation

Standard Deviation Calculator

  Population     Sample

What is Standard Deviation

Standard deviation is a measures of the amount of variation from the average or mean. Deviation means how far a number is from the average. The more spread apart the data, the higher is the deviation.

Calculations

To calcualate Standard Deviation:

Sample number: 1, 2, 3, 4, 5

  1. Find the mean (or average) by adding all the sample numbers and dividing it by the number of samples.

     (1 + 2 + 3 + 4 + 5) / 5 = 3
  2. Find the variance by subtracting each sample numbers with the mean (from step #1), raise it to the power of 2, and then add all the result and divide by the number of samples.

     ((1 - 3)² + (2 - 3)² + (3 - 3)² + (4 -3)² + (5 - 3)²) / 5 = 2
  3. If you are however after the standard deviation equation for a sample of a population, subtract one from the number of samples.

     ((1 - 3)² + (2 - 3)² + (3 - 3)² + (4 -3)² + (5 - 3)²) / (5 - 1) = 2.5
  4. Get the standard deviation by getting the square root of the variance (from step #2 or #3).

Formulas

Whole Population:
σ = √Σ(x - y)² / z Where: σ = Standard Deviation x = each value in the population y = mean of the values z = number of values (population size)

Sample Population:
σ = √Σ(x - y)² / (z - 1) Where: σ = Standard Deviation x = each value in the population y = mean of the values z = number of values (sample size)


Back to top