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Let's say I made several measurements on my gas consumption.

  • $2$ m$^3$ per day
  • $1$ m$^3$ per day
  • $1.5$ m$^3$ per day
  • $2$ m$^3$ per day

What is the average daily consumption of gas?

I can take arithmetic mean and it would be easy, but I've read a text in one statistics book where it says than in case of measurements in the form of per something (like in the above per day) you should use the harmonic mean to find the average.

So which mean should I use here?

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You should be using the arithmetic mean as it would fit best in this situation. Typically, The harmonic mean is used where the numerator of the quantity we're interested is somewhat fixed, for example average speed when you travel from A to B at $x$ kmph and from B to A at $y$ kmph. During this average speed is equal to distance(numerator) divided by time(denominator). here the distance is same during both trips.

The Arithmetic Mean is used when the denominator is a fixed quantity for example if you travel for $1$ hr at $x$ kmph and $1$hr at $y$ kmph.

In this situation the day i.e. denominator is the fixed quantity, so we use Arithmetic Mean.

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  • $\begingroup$ Thank you. Very clear explaination. So if I have colleges A, B and C with 1 professor per 50 students, 1 professor per 60 students, and 1 professor per 70 students I should use harmonic mean to calculate average professor per students ratio (P/S). And if I have 50 students per professor, 60 S/P and 70 S/P, I can use arithmetic mean to calculate average students per professor. Right? (so the two are actually analogous if I invert the given initial ratios) $\endgroup$ – croraf Dec 18 '18 at 21:00
  • $\begingroup$ Yeah, that's right. $\endgroup$ – Sauhard Sharma Dec 19 '18 at 3:36
  • $\begingroup$ Also, would you mind accepting the answer please ? $\endgroup$ – Sauhard Sharma Dec 19 '18 at 3:37

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