Median versus mean

I feel as if I use my husband quite often as the subject in Super Grammar. But it’s because he’s constantly providing fodder.

Today he asked our Amazon Echo, “Alexa, what is the median household income in Kansas City, Kansas?” I asked if he meant average household income, “since there is a difference between median and average.” We began a discussion of the differences and he stated that what he actually wanted Alexa to give him was the arithmetic mean. He’d one-upped the wordsmith!

Let’s take a look at the definitions of these three terms, to see the similarities and differences.

Macquarie Dictionary defines median as:

Median: noun. The middle number in a given sequence of numbers.

In other words, a median is the number that has an equal number of components above it as below it. The median of the set 19, 20, 36 is 20.

So, how do average and arithmetic mean differ from median?

Average: noun. An arithmetic mean.
Arithmetic mean: noun. The mean obtained by adding several quantities together and dividing the sum by the number of quantities.

As you can see, average and arithmetic mean are synonyms and can be used interchangeably. Using the numbers from the example above, the arithmetic mean would be 25.

It’s important to remember the differences between median and average because the answer could vary widely.

Wendy Wood
Proofreader

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