# 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)
```