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).

Select any words here to ask your Maestro about them.

They hire one more person, and now there are 10 salaries. The average is $82,000. How many of the 10 do you think earn less than the average?

Yearly salaries at a small business, in order. The last one is the owner's: it's off the scale, pinned at the top with its number. Example data.

How to find it: sort the values from lowest to highest and take the one in the middle. With 9 values it's the fifth; with 10 there's no single middle one, so the median is the average of the fifth and sixth. In Excel you don't need to sort anything: =MEDIAN(B2:B11).

What it's for: describing the typical case when there are very large or very small values. The median only cares about order, so an outlier doesn't move it, while it does move the average. That's why salaries, home prices and delivery times are better reported with the median.

The median is the line in the middle of a box plot's box. If the average and the median sit far apart, there's a long tail on one side: draw a histogram to see it.

Practice it in Is the average salary what most people earn? and When should you use the average, and when the median?.

How it's used

In Excel

Salaries in B2:B11

marked: =MEDIAN(B2:B11) → 55,500No need to sort: Excel sorts behind the scenes.
=AVERAGE(B2:B11) → 82,000Nine of the ten earn less than this.
=COUNT(B2:B11) → 10Blank cells and text don't count; zeros do.

If someone asks what a typical person earns here, the median answers better than the average.

When to look closer

Is a zero a data point?

This week's sales (closed two days)

1,200 · 1,500 · (blank) · 1,800 · (blank) · 2,100 · 2,400
=MEDIAN(B2:B8) → 1,800

The store was closed two days. If you enter 0 in those cells instead of leaving them blank, does the median change?

Ask your Maestro about Median

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

Example

You: What does "Median" 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 do you report as an average that would read better as a median?

Asking about: Answers from the page "How do I count the missing values in each column with pandas?"

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Median on Wikipedia

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.
Box plot
A box plot sums up a variable in five numbers: the minimum, the first quartile, the median, the third quartile and the maximum. The box runs from the first to the third quartile and holds the middle half of the data.
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.
Weighted average
A weighted average gives each value a weight for how much it counts, instead of treating them all the same: multiply each value by its weight, add them up and divide by the sum of the weights.

The whole glossary