Variance Calculator

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Find Sample and Population Variance

Are you finding it difficult to calculate variance of a statistical dataset? No worries!

Simply enter the dataset values and let this variance calculator calculate variance. Yes, our tool helps you find both sample variance and population variance in seconds. Just enter your dataset, and the tool automatically applies the variance formula to show precise results with steps.

Steps to Using this Variance Calculator

Calculating variance is just like a breeze with this calculator. You need to follow these steps to calculate results!

  1. Enter dataset value, separated by commas
  2. Select type of Variance | Sample or Population
  3. Click or tap ‘Calculate’ to get the result

What Is Variance?

This is the statistical dispersion of data values from their actual mean position.

The variance calculator actually helps you to find this dispersion in terms of numbers that lets you understand the variance statistics easily.

How to Find Variance?

Well, it's quite simple now! 

You have a couple of variance types, as discussed just before. So let’s throw a glimpse at their formulas now.

Sample Variance

\(s^2 = \frac{\sum_{i=1}^{n}(x_i - \bar{x})^2}{n - 1}\)

Where;

  • \(s^{2}\) = Sample Variance
  • \(x_{i}\) = Each value In Sample
  • \(x^{bar}\) = Sample Mean
  • n = Number of Provided Values

Population Variance

\(\sigma^2 = \frac{\sum_{i=1}^{N}(x_i - \mu)^2}{N}\)

Where;

  • \(σ^{2}\) = Population Variance
  • \(x_{i}\) = Each value In Population
  • \(μ\) = Population Mean
  • N = Number of Provided Values

Example

Given Data

\( \{5, 7, 9, 10, 14\} \)

Solution

Step 1: Calculate the Sample Mean  

\( \bar{x} = \dfrac{5 + 7 + 9 + 10 + 14}{5} = 9 \)

Step 2: Subtract the Mean from Each Value  

\( 5 - 9 = -4 \)  
\( 7 - 9 = -2 \)  
\( 9 - 9 = 0 \)  
\( 10 - 9 = 1 \)  
\( 14 - 9 = 5 \)

Step 3: Square Each Deviation  

\( (-4)^2 = 16 \)  
\( (-2)^2 = 4 \)  
\( 0^2 = 0 \)  
\( 1^2 = 1 \)  
\( 5^2 = 25 \)

Step 4: Add the Squared Deviations  

\( \sum (x - \bar{x})^2 = 16 + 4 + 0 + 1 + 25 = 46 \)

Step 5: Divide by \( n - 1 \) to Find Sample Variance  

\( s^2 = \dfrac{46}{5 - 1} = \dfrac{46}{4} = 11.5 \)

Faqs

What is the difference between variance and standard deviation?

Variance measures how far each data point is from the mean, while standard deviation shows the same spread in the original units of the data.

Can I find both variance and standard deviation with this tool?

Yes. This variance calculator automatically finds both variance and standard deviation for your data set.

When you enter your numbers and click calculate, it displays:

  • The mean (average)
  • The sample or population variance
  • The standard deviation (square root of variance)
  • You can use it for both small samples and full population data.

How accurate is this online variance calculator?

This variance calculator is fully accurate because it uses the official statistical formulas for both sample and population variance.

All calculations are handled by precise mathematical operations, ensuring that the results match what you’d get in Excel or a statistics textbook. It also works for decimal numbers and negative values without any rounding errors in intermediate steps.

Is this variance calculator free to use?

Yes. This variance calculator is 100% free and available for unlimited use.