---
title: "Variance Calculator — Population & Sample Variance (÷n vs ÷n−1)"
description: "Calculate variance from a data set — both population (÷n) and sample (÷n−1). Includes the step-by-step deviation table and standard deviation. Explains Bessel's correction and curriculum differences."
url: "https://worldcalculators.org/calculators/variance/"
canonical: "https://worldcalculators.org/calculators/variance/"
---

# Variance Calculator

Calculate variance from a data set — both population (÷n) and sample (÷n−1). Includes the step-by-step deviation table and standard deviation. Explains Bessel's correction and curriculum differences.

## Quick answer

In Japan and China's high school curricula (数学B / 高中数学), descriptive statistics focuses on characterising a given data set rather than making inferences about a broader population. Since the data set in hand IS the "population" being described, dividing by n is appropriate. When students reach university-level statistics, they learn sample variance (÷n−1). US and UK curricula prioritise inferential statistics from early on, so ÷n−1 is introduced first.

## Frequently Asked Questions

In Japan and China's high school curricula (数学B / 高中数学), descriptive statistics focuses on characterising a given data set rather than making inferences about a broader population. Since the data set in hand IS the "population" being described, dividing by n is appropriate. When students reach university-level statistics, they learn sample variance (÷n−1). US and UK curricula prioritise inferential statistics from early on, so ÷n−1 is introduced first.
Python's numpy uses population formula by default: numpy.std(data) divides by n. For sample standard deviation, use numpy.std(data, ddof=1). Python's statistics module uses sample formula by default: statistics.stdev(data) divides by n−1. pandas DataFrame.std() also uses n−1 by default. R's sd() function uses n−1. Always check the ddof (delta degrees of freedom) parameter.

Source: https://worldcalculators.org/calculators/variance/
Markdown mirror of the HTML page. Prefer this URL for RAG; the interactive calculator still lives on the HTML page.