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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.

Select any words here to ask your Maestro about them.

At A, the standard deviation is 1.8 minutes. B has the same 30-minute average, but its deliveries run from 16 to 44. About how big do you think B's standard deviation is?

Ten orders from each branch. The dashed line is the average: 30 minutes at both. Example data.

What it tells you: how far from the average your data usually lands. A small standard deviation says nearly everything looks like the average; a big one says the average is hiding a lot of spread. Two branches can both average 30 minutes and be nothing alike, as in the figure.

How to calculate it: find the average, measure how far each value is from it, square those distances, add them up, divide by n − 1 and take the square root. In Excel it's =STDEV.S(B2:B11). What you have before the square root is the variance.

If your data is bell-shaped, about two out of three values fall within one standard deviation of the average. If there are outliers, the standard deviation grows a lot, so look at the median and a histogram too.

See why spread matters in Why do small towns have the highest (and lowest) rates?.

How it's used

How to calculate it

Four deliveries: 26, 28, 32, 34 minutes

  1. Average: 120 ÷ 4 = 30
  2. Distance from the average: −4, −2, +2, +4
  3. Squared and added up: 16 + 4 + 4 + 16 = 40Squared, the ones below no longer cancel the ones above.
  4. Divide by n − 1: 40 ÷ 3 = 13.33That's the variance.
  5. marked: Square root: √13.33 = 3.65 minutes
  6. In Excel: =STDEV.S(B2:B5)The .S is for a sample, the one you almost always want.
The square root brings the number back to minutes, so you can read it like this: these deliveries usually land about 3.7 minutes from the average.

When to look closer

STDEV.S or STDEV.P?

Four deliveries in B2:B5

  1. marked: =STDEV.S(B2:B5)
  2. marked: =STDEV.P(B2:B5)

With the same four numbers, do you think STDEV.S and STDEV.P give the same answer?

Ask your Maestro about Standard deviation

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

Example

You: What does "Standard deviation" mean, in plain words?

Your Maestro: I'll explain it with a case of yours: it sticks better than a definition. Which average do you report at work that hides a lot of spread?

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

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Related terms

  • 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.

  • 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).

  • 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.

  • Histogram

    A histogram shows how the values in a column of numbers are spread out: it cuts them into ranges of equal width and draws one bar per range, as tall as the number of values that fall in it.

The whole glossary