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Variance

Variance measures how spread out data is: it averages the squared distances from the mean. Its square root is the standard deviation.

Select any words here to ask your Maestro about them.

Four deliveries take 26, 28, 32, 34 minutes; the average is 30. To measure how spread out they are, why isn't it enough to add up how far each one landed from the average?

Four deliveries; the average is 30 minutes. Example data.

What it measures: how spread out the data is around the average. If the values are all alike, the variance is small; if they're scattered, it's big.

How to calculate it: find the average, subtract it from each value, square each difference, add them up and divide by n − 1 (or by n if you have the whole population). In Excel: =VAR.S(B2:B11), or =VAR.P for a whole population.

It comes out in squared units (minutes², dollars²), so it's rarely reported on its own: its square root is the standard deviation, back in your data's units. An outlier inflates it a lot.

See why spread matters in What does an average hide? Mean vs. median.

How it's used

Variance or standard deviation

The same four deliveries: 26, 28, 32, 34 minutes

  1. Variance: 13.33 min²=VAR.S(B2:B5). Minutes squared: nobody can picture that.
  2. marked: Square root: √13.33 = 3.65 min=STDEV.S(B2:B5). Back in minutes.
  3. Read it like this: deliveries usually land about 3.7 minutes from the average.
Variance is the middle step: it's what you calculate with (variances can be added up). To tell someone how spread out your data is, use its square root, the standard deviation.

When to look closer

One extreme value blows up the variance

B2:B5 = 26, 28, 32, 34

  1. marked: =VAR.S(B2:B5)
  2. 13.3

The variance is 13.3. If a fifth delivery takes 60 minutes, how much do you think it grows?

Ask your Maestro about Variance

It answers from the free course page closest to this word, the way it answers while you study.

Example

You: What does "Variance" mean, in plain words?

Your Maestro: I'll explain it with a case of yours: it sticks better than a definition. Which number at work varies so much that the average alone isn't enough?

Asking about: Answers from the page "What does an average hide? Mean vs. median"

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Related terms

  • Standard deviation

    Standard deviation measures how far data lands from the average: with an average of 30 and an SD of 2, most values fall from 28 to 32. In Excel: =STDEV.S.

  • Mean (average)

    To find the mean (the average), add up all the values and divide by how many there are: 15, 7, 8, 13 and 7 add up to 50, and 50 ÷ 5 = 10.

  • Outlier

    An outlier is a value that sits far from the rest, like a $9,800 order among $300 ones. It can be a data-entry error or a real, important case: before you drop it, find out which.

  • Median

    The median is the middle value when you sort the data from lowest to highest: half sit below it and half above. In Excel you get it with =MEDIAN(B2:B11).

The whole glossary