This Variance Calculator computes the Sample Variance and Population Variance

Select the Data Set: -

Population size:
Mean (μ):

Variance Calculator’s Instructions:

1. First of all select the data type for which you want to find variance
2. Put Data values, separated by commas (,) or Enter.
3. Click on [Calculate] button.
4. Variance Calculator will show result without refreshing the page.
5. To get a result for another data set please Press the [Reset] button.

Sample Variance Calculator (Instructions):

You can also use this Variance Calculator as a Sample Variance Calculator by following steps:

• Select the Sample Variance
• Put Data
• Press [Calculate] button.
• To Put data again or to calculate the population variance please press the [Reaset] button first.

Population Variance Calculator (Instructions):

• Select the Population Variance
• Put Data
• Press [Calculate] button.
• To Put data again or to calculate the sample variance please press the [Reaset] button first.

What is Variance?

According to probability theory and statistics, a variance is the probability of the squared deviation of a random variable from its mean. Casually, it measures how far a set of (random) numbers are spread out from their average value. Variance has a vital role in statistics, where some ideas that use it include expressive statistics, statistical supposition, hypothesis testing, goodness of fit, and Monte Carlo sampling. A variance is a vital tool in the sciences, where statistical analysis of data is ordinary.

variance Sign

Variance Calculator Formula:

Variance Calculator Formula

Sample Variance Calculating Formula:

Sample Variance Calculator Formula

Population Variance Calculating Formula:

Population Variance Calculator Formula

Example

Sample question: Find the population variance of the age of children in a family of five children aged 16, 11, 9, 8, and 1:

Step 1: Find the mean, μx:
μ = 9.

Step 2: Subtract each data point from the mean, then square the result:
(16-9)2 = 49
(11-9)2 = 4
(9-9)2 = 0
(8-9)2 = 1
(1-9)2 = 64.

Step 3: Add up all of the squared differences from Step 2:
(16-9)2 + (11-9)2 + (9-9)2 + (8-9)2+ (1-9)2 = 118.

Step 4: Divide Step 3 by the number of items. 118/5 gives a population variance of 23.6.