# Sample Variance Calculator

Calculate sample variance with the n - 1 denominator for estimating spread from a sample dataset

> Canonical page: https://elysiatools.com/en/tools/sample-variance-calculator

- **Category:** Math & Numbers

- **Keywords:** sample variance, variance, statistics, n-1, spread, descriptive statistics

## Overview

Calculate sample variance for a numeric dataset.

Sample variance uses the n - 1 denominator:

s^2 = sum((x - xbar)^2) / (n - 1)

Use it when your data is a sample taken from a larger population and you want an unbiased estimate of population spread.

## Inputs

- **Dataset** (textarea): e.g. 10, 12, 23, 23, 16, 23, 21, 16
- **Decimal Places** (number)
- **Include Squared Differences** (checkbox)

## When to use

- When analyzing a subset of data (a sample) to estimate the variability of a larger population.
- When conducting statistical hypothesis testing or calculating confidence intervals that require sample variance.
- When evaluating the consistency or spread of experimental results, survey responses, or quality control measurements.

## How it works

- Enter your numeric dataset into the text area, separating each value with a comma.
- Specify the desired number of decimal places for the final variance calculation.
- Toggle the option to include squared differences if you need to see the intermediate calculation steps for each data point.
- The tool applies the n-1 formula and outputs the sample variance in a structured JSON format.

## Use cases

- Quality control analysts measuring a random batch of manufactured parts to estimate overall production consistency.
- Researchers analyzing survey data from a sample group to infer the variability of opinions in the broader public.
- Students verifying manual statistics homework involving the n-1 sample variance formula.

## Frequently asked questions

### What is the difference between sample variance and population variance?

Sample variance divides the sum of squared differences by n-1 to provide an unbiased estimate of the population. Population variance divides by n and is used only when you have data for the entire population.

### How should I format my dataset?

Enter your numbers separated by commas. For example: 10, 12, 23, 23, 16.

### What does the 'Include Squared Differences' option do?

When enabled, the output will include the squared difference from the mean for each individual data point, which is helpful for verifying manual calculations or understanding the data spread.

### Can I adjust the precision of the result?

Yes, you can set the 'Decimal Places' option to round the final sample variance to your preferred number of decimal digits, up to 10 places.

### Why is my sample variance so high?

A high sample variance indicates that the data points in your sample are spread out widely from the mean. Outliers can significantly increase the variance.

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