# What is the better term for “average of monthly average over years”?

Assume we got a monthly average data from Jan to Dec of Year 2012. Then we got another monthly average data from Jan to Dec of Year 2013. If we average the monthly average of both year, for example

new average of Jan = (jan of Year 2012 + Jan of Year 2013)/2,

new average of Feb = (Feb of Year 2012 + Feb of Year 2013)/2,

...

new average of Dec = (Dec of Year 2012 + Dec of Year 2013)/2,

do we have a more consolidated term for this?

• Mathematically isn't this equivalent to averaging the monthly data for the 24 month period? You could call it a "two-year monthly average" – mstorkson Jan 30 '17 at 18:43
• @mstorkson Ideally they would be equivalent, but an "average of averages" could be introducing rounding error which would not be present in the simple, longer-term average. For example, assume the monthly averages have all been rounded up to the nearest integer, and then you re-average all those integers. (It is awkward to say the average family size has "2.3 children", but you don't want to ignore the "more than two". So you might say "3".) This average will end up higher than the long term average. That said, a long term average would likely be the better way to handle it. – RichF Jan 31 '17 at 0:25
• @mstorkson You answer seems what I am looking for. Since we have terms like monthly average and average monthly for some specific statistics. I want to see what other expression can I use to discuss the above statistics or how can we express it clearly in general. – user2720402 Jan 31 '17 at 3:32
• @mstorkson Please add some references if possible. thanks – user2720402 Jan 31 '17 at 3:51
• The monthly average for 2000 to 2015. For example. – Lambie Jan 31 '17 at 15:50

You can call it an "average of averages" but I think anyone who understands the basic math would want to correct this to a simple "average" since the math is the same either way:

``````(2012_total/12 + 2013_total/12) * 1/2 == (2012_total + 2013_total)/24
``````

[Update] If you want to average individual months over several years, you can call it a "month-by-month average from 2012 to 2013". There still may be some confusion what you mean, in which case you'll need to show the math.

• You may get me wrong. Please see the edits. I don't want to average all different months and years. I just want the average of different years of the same month. – user2720402 Jan 31 '17 at 3:50
• Ok, updated my answer. – Andrew Jan 31 '17 at 15:46

The simplest way to describe this is

average of calendar months for 2012 and 2013

Since you want to average all the Januarys, together and Februarys together, etc. I suppose you are doing this to see seasonality.