Understanding Variance

Variance measures how far a set of numbers are spread out from their average value. It's a fundamental concept in descriptive statistics, quality control, and risk management.

Calculation Steps

Calculate the mean (average) of the dataset
Subtract the mean from each data point and square the result
Sum all squared differences
Divide by N (population) or N-1 (sample)

Example Calculation

For dataset [4, 7, 9, 10, 15]:

Mean: (4+7+9+10+15)/5 = 9
Squared differences: (4-9)²=25, (7-9)²=4, (9-9)²=0, (10-9)²=1, (15-9)²=36
Sum of squares: 25+4+0+1+36 = 66
Population variance: 66/5 = 13.2
Sample variance: 66/4 = 16.5

Frequently Asked Questions

When should I use population vs sample variance?

Use population variance when your dataset includes all members of a population. Use sample variance when working with a sample from a larger population.

Why are there different formulas for variance?

Sample variance uses Bessel's correction (dividing by n-1 instead of n) to reduce bias when estimating population variance from a sample.

What's the relationship between variance and standard deviation?

Standard deviation is the square root of variance, providing a measure of spread in the same units as the original data.

Variance Calculator

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Data Distribution Visualization

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Variance Calculator - Measure of Spread

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