### How to Use Variance Calculator

Select Sample Variance or Population Variance.

Enter the data set with numbers separated by a comma, for example a data set looks like 1,5,6,7

Press Calculate

# Variance Calculator

### How to calculate Variance

Below are the steps used to calculate the variance- Calculate what the mean is of the data set(the simple average of all the numbers)
- For each number, subtract the mean and then square the result
- Work out the average of the squared differences

**Sample Variance**

- Our Data set is: 6,12,7,9,2
- First, sum up all the numbers 6 + 12 + 7 + 9 + 2 = 36
- Then divide by the amount of numbers in the data set to get the mean 36/4 = 9
- Now for each number we subtract the mean and then square the result: (6 - 7.2), (12 - 7.2), (7 - 7.2), (9 - 7.2), (2 - 7.2)
- Since we are getting the sample variance we take 1 away from the amount of numbers in the data set when dividing the squared differences
- Squared differences `((-1.2)^2 + (4.8)^2 + (0.2)^2 + (1.8)^2 + (-5.2)^2)/(5 -1) = 13.7`
- Sample variance: 13.7

Example 2:

**Population variance**

- Data set is: 10, 12, 16, 20, 22, 10
- First, sum up all the numbers: 10 + 12 + 16 + 20 + 22 + 10 = 90
- To get the mean we divide 80 by the amount of numbers in the data set: 90/6 = 18
- With each number we subtract the mean and square the result: (10 -15), (12 - 15), (16 - 15), (20 - 15), (22 - 15), (10 - 15)
- Since this time we are getting the population variance we do not add -1 when dividing the squared differences
- `((-5)^2 + (-3)^2 + (1)^2 + (5)^2 + (7)^2 + (-5)^2)/6 = 22.33`
- The population variance is 22.33

**Variance Definition**:The average of the squared differences from the Mean.
.
Variance is used as a form of measurement of the spread between numbers in any given data set. By measuring the difference there is for each number in the data set from the mean. It gives a general idea of how spread the data set is.

If the variance is zero this means there is no variability and all the numbers in the data set are the same. While a low variance means there is a small change in the data set but most are the same or are very close to each other. A large variance is when the numbers in the data set are very different from each other.

### Population Variance and Sample Variance

Population is when all members or info is used, such as the whole population of a country when measuring weight etc.A sample variance is a part of the population that is used, the sample could be 2% 25% or higher but never the whole population. For example to measure the average height in America, it wouldn't be an easy task from a money or time point of view, therefore a sample of the population is used, lets say around 2,000 people and that sample size is used.

**Population Variance**

- Data Set: 5, 5, 5, 5, 5 = 0 Variance.
- Data Set: 5, 5, 6, 5, 4 = 0.4 Variance.
- Data Set: 5, 125, 5, 1, 200 = 6619.36 Variance

**Sample Variance**

- Data Set: 5, 5, 5, 5, 5 = 0 Variance.
- Data Set: 4, 5, 5, 5, 6 = 0.5 Variance
- Data Set: 5, 125, 5, 1, 200 = 8274.2 Variance