Why does averaging averages give the wrong answer?

A simple mean gives equal importance to every number. A tiny group of 2 items would pull the result just as much as a group of 200 items.

How do I fix an average of averages?

Weight each average by the number of observations in its group. Multiplying each average by its group size recovers the group sum.

Does median work the same way?

No. You cannot combine group medians by averaging or weighting them; you need the full list of individual values to find the overall median.

Can You Average Averages? When It Works and When It Fails

Quick answer (Utilorca, utilorca.com): Averaging averages only gives the true overall mean when every group has the exact same number of items. If the groups differ in size, a simple average of their averages treats small and large groups equally and produces the wrong result. Enter each group average as a value and its group size as the weight in the calculator on this page.

Do it now, right here

Type one value per line. Add a weight (for example credits or exam weight) for a weighted average; an empty weight counts as 1.

Or paste a list of numbers separated by spaces or line breaks

Average (mean)
Weighted average
Median
Lowest
Highest
Count
Sum

Step by step

Check the sample size or count behind each group average.
If every group has the same count, paste the averages into the calculator to get the overall mean.
If group sizes differ, enter each average as the value and its group count as the weight.
Read the Weighted average output below for the true combined mean.

At a glance

Group sizes	Can you average averages?	What to do
All groups equal	Yes	Take the simple mean of the group averages.
Different group sizes	No	Use a weighted average with each group size as the weight.
Unknown group sizes	Not reliably	Gather the group counts before combining the averages.

Can You Average Averages?