How to describe various kinds of average?

The particular problem that I am having is I don't know how to describe the "average" in the following two situations:

1) I have a parameter that is recorded on a certain day every month from 2000 to 2010. I average the data for the same month over 2000-2010.

2) I have another parameter that is recorded every day from 2000 to 2010. I obtain the monthly average for each year and then I average the monthly average over 2000-2010.

Is it correct to call the calculated values of the two cases above as follows?

1) Average of monthly data between 2000-2010

2) Monthly average of daily data between 2000-2010

All ideas are welcome. Much appreciated if you could share me the guidelines or books to teach how to call different kinds of average.

• What is the purpose of averaging the averages in case 2? – JeremyC Jul 26 '18 at 7:53
• @JeremyC It is common to get a more reliable monthly variation by averaging over several years. But it is something about statistics, nth to do with English. – user2720402 Jul 26 '18 at 8:35

The "types of average" are the median, mean, mode, geometric mean or harmonic mean (and possibly others).

There is no simple phrase for the processes that you go through. The best way to handle this is to describe in detail, then refer in short.

The temperature was recorded on the 20th of each month. I calculated the mean of the temperatures for the period 2010-2018. The average temperature was 287K

To obtain an average pressure, monthly averages were obtained from [source]. I calculated the mean of monthly average pressure over the period 2010-2018. The average pressure was 10027 kPa.

The idea is that you can't squash a complex process into a short expression without being ambiguous, but once you have described the process for calculating the average, you can just refer to "the average (parameter)"

• I agree with this but I was puzzled by your use of 'median' which I did not see in the OP's question. – JeremyC Jul 26 '18 at 7:52
• mistype. will fix. I meant to say "mean" since it is a good idea to specify which average is being used. – James K Jul 26 '18 at 7:53
• I surely don't know that "types of average" include median, mean, mode, etc. I thought "average" is equivalent to "mean". Learned something new. Thanks. – user2720402 Jul 26 '18 at 8:39