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What is Variance in Statistics?

If you work with statistics, you've likely encountered the term variance. Maybe you've asked yourself — what is variance in statistics?

When it comes to the variance definition, it is tightly connected to the nature of the dataset, or more precisely, how the values in your dataset are spread.

In this article, you can find out more about the topic, including:

  • The variance formula;
  • How to calculate variance; and
  • Variance meaning — value interpretation and practical application.

Variance is the degree of variability within a dataset. In other words, it tells you how far the data points are from the mean, making it a measure of data variability.

  • A low variance means the values are clustered closely around the mean; and
  • A high variance means they are more spread out.

It essentially shows to what extent members of a group differ from one another.

Scientifically speaking, variance is the expected value of the squared deviation of a random variable from its mean, which brings us to how to calculate variance.

If you want to know how to calculate variance, you just need to follow these steps:

  1. Find your dataset.
  2. Take the difference between each value and the mean.
  3. Square these differences.
  4. Divide their sum by the total number of values.

Depending on the scenario, you must use one of the two variance equations:

Variance equation for a population:

σ2=∑i=1N(xi−μ)2N\sigma^2 = \frac{\sum_{i=1}^N (x_i - \mu)^2}{N}

where:

  • σ2\sigma^2 — Population variance;
  • xix_i — Each individual data point;
  • μ\mu — Population mean; and
  • NN — Number of data points in the population.

Variance equation for a sample:

s2=∑i=1n(xi−xˉ)2n−1s^2 = \frac{\sum_{i=1}^n (x_i - \bar{x})^2}{n - 1}

where:

  • s2s^2 — Sample variance;
  • xix_i — Each data point in the sample;
  • xˉ\bar{x} — Sample mean; and
  • nn — Number of data points in the sample.

You may also use our variance calculator 🇺🇸 to calculate variance or to double-check your results.

Now that we've clarified what variance is and how it is calculated, let's look at how to interpret the results:

  • Variance value closer to zero (smaller magnitude) — this means the numbers are tightly clustered around the center; or
  • Variance value farther from zero (larger magnitude) — some numbers in the dataset are far from the center.

Additional points to keep in mind:

  • Variance can never be less than zero; and
  • Variance equals zero only when all numbers in the dataset are identical.

Beyond being a summary statistic, variance is also commonly used in other statistical analyses, such as constructing confidence intervals.

Since variance measures how spread out a set of numbers is, it is one of the most widely used concepts in statistics, which has implications in almost every field that relies on data, such as:

  • Health — understanding lab results, vital signs, and stable medication dosing;
  • Finance — measuring investment risk, spending habits, and insurance premiums;
  • Education — checking test score consistency and school performance;
  • Work & business — forecasting sales, costs, and customer behavior;
  • Sports & fitness — tracking performance consistency and training results.
  • Everyday decisions — comparing products, monitoring diet or routines, and planning budgets.

In statistics, variance is a measure of consistency of values within a dataset. It shows how far each data point is from the mean and from every other point on average. A low variance means the data points are close together, while a high variance means they are more widely dispersed. Mathematically speaking, it’s the average of the squared differences between each value and the mean.

Depending on the type of data you have, you need to use the appropriate variance formula:

  • Population variance (σ²):

σ² = [ Σ (xi − μ)² ] / N

or:

  • Sample variance (s²):

s² = [ Σ (xi − x̄)² ] / (n − 1)

where:

  • xi — Individual data point;
  • μ — Population mean;
  • N — Number of data points in the population;
  • x̄ — Sample mean; and
  • n — Number of data points in the sample.

If you want to calculate variance, follow these easy steps:

  1. Start with your dataset.
  2. Calculate the mean.
  3. For each value, find its deviation from the mean.
  4. Square these deviations.
  5. Add them up and divide by the number of values.

Or simply use our variance calculator.

Variance describes the degree of variability in a dataset, showing how far data points lie from the mean and reflecting overall consistency. A low variance indicates values are closely clustered, while a high variance means they are more widely spread. In statistical terms, variance is the expected value of the squared deviations of a random variable from its mean.

This article was written by Julia Kopczyńska and reviewed by Steven Wooding.