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I have trouble understanding if I should use "monthly average" or "average per month" when asking someone to calculate monthly average of a variable, e.g. heating expenses. Is there any difference, if this payment happens every month or quarterly, and I want to know average per month?

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Average per month" or ("average monthly") and "monthly average" (or "monthly mean") have different meanings.

Rather than speak about the "Average per month" it would be clearer to use "average cost per month". It can be used and calculated as follows:

  • For payments that are made every month - add up all the money spent on electricity during 12 months then divide by 12 to get the average per month (http://www.ehow.com/how_6391683_calculate-average-monthly-return.html)
  • For payments that are made at intervals greater than monthly divide by the number of months in the interval (eg. for electricity bills that come every quarter, divide the amount paid last quarter by 3 to get the Average per month.)
  • For amounts that are calculated more frequently than each month where you want to know the average you spend per month (eg Perhaps your phone bill lists your charges for each day, then to find the average per month you would add up, say, the 365 daily charges for a calendar year than divide by 12 to find the average per month.)

Monthly average (or monthly mean) would be used for something that is recorded more frequently than once per month when you want to know the average value of that quantity during a month. (http://www.answers.com/Q/How_do_you_calculate_monthly_average_balance) For example:

  • If your phone bill lists your charges for each day you would find the monthly average of your daily phone charges by adding up the daily charges for the days of, say, July and then divide by 31 ( as there are 31 days in July)

Unfortunately "monthly average" is not always used correctly (http://stats.oecd.org/glossary/detail.asp?ID=3722) It is best to state explicitly what quantity is to be averaged, as in the above example ("monthly average of your daily phone charges") so that your meaning is clear.

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    I won't say whether I agree or disagree with these statements, but you do need to back them up by citing some external authorities on the matter, or at least cote unambiguous examples of people using the phrases this way. – Dan Bron Nov 24 '14 at 12:04
  • @DanBron I have noted your comment, however I have edited my answer since you made it and believe it no longer applies. What is needed now are references to examples that confirm the mathematics of the examples I have given. These are not easy to find but I will keep looking. – JoAnne Nov 24 '14 at 14:11
  • Thanks Joanne. Your answer is definitely improved, but I think what's lacking is not confirmation of the mathematics, but confirmation of the interpretations you've given to these phrases (and validation that the two meanings couldn't, for example, be switched). – Dan Bron Nov 24 '14 at 14:17
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    @DanBron I disagree, these are mathematical concepts. As someone who taught mathematics for several years, at higher secondary level where "word questions" are very important, I know what the terms mean. Mathematical language is not well understood by many people. People may mistakenly use "monthly average" when they actually want the 'average per month' but that doesn't change the meaning of those terms, just as people writing about "stationery cars" does not change the meaning of "stationery" or "stationary". – JoAnne Nov 24 '14 at 15:10
  • JoAnne, that's all well and good; just find some reliable mathematical sources which support the interpretations you are promoting. – Dan Bron Nov 24 '14 at 15:13
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Suggestions to Authors of the Reports of the United States Geological Survey, Fifth Edition, 1958, page 44, says, "The terms "daily mean" and "mean daily" should not be used indiscriminately, nor should "monthly mean" and "mean monthly," "annual mean" and "mean annual," etc. The daily mean discharge for any day is defined as the mean discharge for that one day; the mean daily discharge for any one day, October 10, for instance, is the arithmetic mean of the discharge on all October 10's of record, or during a specific period of years. Likewise, the monthly mean discharge for October 1951 is simply the arithmetic mean of the 31 individual daily mean discharges during that month, whereas the mean monthly discharge for October is the arithmetic mean of all October means of record or during a specific period of years."

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For my electricity or gas bill, I would say:

My electricity bill is about $250 per month, on (the) average.

On (the) average, I spend $250 per month on gas heating.

"monthly average" is better used for "exchange rates", "temperatures", "rain and snowfall", prices, etc.

  • "rain and snowfall" are tricky ones. In areas of high rainfall the "monthly average of the daily rainfall" might be quoted, but in areas with low rainfall the "average rainfall per month" might be quoted. – JoAnne Nov 25 '14 at 0:29

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