# Variance

Updated July 11, 2021

## What is Variance?

Variance is a statistical measure of how much a set of observations differ from each other.

In accounting and financial analysis, variance also refers to how much an actual expense deviates from the budgeted or forecast amount.

## How Does Variance Work?

For example, let's say Company XYZ stock has the following prices: The average of these prices is \$21.33. To calculate the variance, we see how "far away" each day's stock price is from \$21, like this: Notice that some of the differences are negative. Because we're going to calculate the average difference, the negative numbers create a mathematical problem (they'll offset the positive numbers and screw up the calculation). To avoid this, we square each difference so that each difference is positive, like this: The last step is simply calculating the average of those squared differences, which is \$9.42, and then taking the square root of that number to get the amount by which Company XYZ stock tends to vary from its average price.

The square root is \$3.07, meaning that when Company XYZ deviates from that \$21 average, it tends to do so by about \$3.07.

## Why Does Variance Matter?

Variance is a measure of volatility because it measures how much a stock tends to deviate from its mean. The higher the variance, the more wildly the stock fluctuates. Accordingly, the higher the variance, the riskier the stock.

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