# Calculating an average of other averages

This is purely for interest, but so far Googling has come up empty.

Given the following dataset of the number of items bought in a fictional shop, is there a way of calculating the figure in yellow by only using the figures in pink?

I know taking the average of the figures in pink will give me the wrong result(in this case 3.22), but was wondering whether there's a mathematical way of doing this. I have tried searching for the answer, but can't seem to find anything. Maybe it's just me...

• You can take a weighted average of the pink column (using Total Customers as the weights) to get the yellow number – Henry Jan 16 '18 at 11:42

Consider these two tables:

ip     cust      ipc
44       2        22
100      10       10
--------------------
144      12       12

ip     cust      ipc
440      20       22
10        1       10
---------------------
450      21       21.42...


The numbers corresponding to the ones you marked in pink are identical in the two tables, but the desired results (in the lower right) differ. Hence you cannot get the number in the lower right just from the pink numbers.

If you're willing to include the number of customers (or the items per customer), i.e., the data from either the first OR the second column, then you can reconstruct the missing column, and find the answer. But without those --- there's no hope.