On Average, Mean, Median, and Mode

If you’re reading this you’re probably a bit geeky (like me), and you’ve no doubt been in at least 42 conversations about average vs. mean, etc, etc. So here’s a good summary of the basics for next time.

First Things First: “Average” is a General Term

If you’ve ever been lobbed the question of “what’s the difference between the average and the mean?”, you (and perhaps the questioner too) might have fallen into a trap. A mean is a type of average, not an alternative to one.

average

- An average is a single value that is meant to typify a list of values.

Average is a general class. It just means “let’s try and generalize the data given a set of data points”, and the (basic) mechanics for actually doing so are described with three other terms: *mean*, *median*, and *mode*.

mean

- A mean is attained by adding all values and dividing by the total number of values.

Hey, wait–that sounds like an average, right? That’s because it is. That’s the whole point–they’re the same. A mean is a type of average, so when people are asked to give an average (a general idea of the data) they often give the mean. And what about median and mode?

median

- A median is described as the numeric value separating the higher half of a sample, a population, or a probability distribution, from the lower half.

Simple enough. And what about mode?

mode

- The mode is the value that occurs the most frequently in a data set or a probability distribution.

Summary

Means, medians, and modes are all types of averages. A mean is the one where you add them all up and divide by the number of values, the median is the value that separates the top half and bottom half, and the mode is the value that is found most frequently in the set. ::

Notes

¹ [ For more reading, do visit the averages page at Wikipedia. ]