# Population Variance Calculator

Calculate population variance with the n denominator for a complete numeric dataset

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

- **Category:** Math & Numbers

- **Keywords:** population variance, variance, statistics, n denominator, spread, descriptive statistics

## Overview

Calculate population variance for a complete numeric dataset.

Population variance uses the n denominator:

sigma^2 = sum((x - mean)^2) / n

Use it when your dataset represents the entire population you want to describe, such as all items in a batch or all scores in a class.

## Inputs

- **Dataset** (textarea): e.g. 2, 4, 4, 4, 5, 5, 7, 9
- **Decimal Places** (number)
- **Include Sample Comparison** (checkbox)

## When to use

- When analyzing a complete dataset where every member of the target group is accounted for.
- When calculating the exact spread or dispersion of all items in a specific batch or class.
- When studying descriptive statistics that require the standard n denominator formula.

## How it works

- Enter your complete numeric dataset into the text area, separating values with commas, spaces, or newlines.
- Specify the number of decimal places you want in the final result.
- Toggle the sample comparison option if you want to see the difference between population and sample variance.
- The tool calculates the mean, subtracts it from each value, squares the differences, and divides the sum by n to output the population variance.

## Use cases

- Teachers calculating the variance of test scores for an entire classroom of students.
- Quality control managers measuring the consistency of a complete production batch.
- Researchers analyzing demographic data collected from an entire localized population.

## Frequently asked questions

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

Population variance divides the sum of squared differences by n (the total number of items), while sample variance divides by n-1 to correct for bias when estimating from a sample.

### When should I use population variance?

Use it when your dataset includes every individual or item in the group you are studying, rather than a smaller subset drawn from a larger group.

### How should I format my dataset?

You can enter numbers separated by commas, spaces, or newlines. The calculator will automatically parse the numeric values.

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

Yes, you can configure the decimal places setting to round the calculated variance to anywhere between 0 and 10 decimal places.

### What does the include sample comparison option do?

It calculates and displays the sample variance alongside the population variance, allowing you to easily compare the results of both formulas.

## Related tools

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