Can you average averages

Oftentimes the best that can be done if a regional median value is absolutely necessary, is to go ahead and average it.

In those cases, be sure to call it the average median value instead of a median value. March-April vol. Inside this Issue March-April vol. Attempting to average existing averages without knowing the number of values contained in each value leads to statistical errors. Either use the original values or keep hold of the number of values included in the average in order to keep your numbers accurate.

Written by Steve Fenton on 14th February Can you average averages in your analytics? Average of averages If you wanted to see an average customer score across all coffee shops, you might be tempted to sum the two averages and divide them by 2.

How do we resolve this imbalance? Original numbers If you have all of the original scores, you can get an accurate average by totalling up all the scores and dividing the total by the number of scores submitted. Summary Attempting to average existing averages without knowing the number of values contained in each value leads to statistical errors. In the example above, an average position of When combining calculated metrics like these, the size of each group is important — combining a small sample into a larger sample should not affect the overall average much it should be closer to Searching for a typical formula for a weighted average yields something like this — you multiply each average by a weighting factor that is calculated from the proportion of the impressions they represent, then add them together:.

Just describing it sounds complicated, and this formula is hard to implement , especially with large data sets. That is a lot of lookups and calculations, and it could be very slow. As an example, let's say that an assessment is given to three schools and I want to find out the average score for all three schools combined and the average score per school. If a school system created a small school consisting of all the smartest students, they could bump up the second value - the "average of averages" - but they couldn't do that if they take the correct weighted average.

I hope this is enough to explain what goes wrong you're giving equal weights to the "first averages" when you take their average, which isn't the correct thing to do if you want the average of all the numbers. Thomas Andrews already answered the question, but I'd like to present a more analytical solution to the problem.

This answers the first OP question, as to why the average of averages usually gives the wrong answer. This is why the average of averages is equal to the average of the whole group when the groups have the same size. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. Why is an average of an average usually incorrect?

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