What is the application of harmonic mean in medicine?

Answer 1

By definition, the harmonic mean of a dataset (x1, x2, ..., xn) is the reciprocal of the arithmetic mean of the dataset's reciprocals.

That is, MeanHarmonic=n/[1/x1+1/x2+...+1/xn]

The harmonic mean applies more accurately to certain situations involving rates. For example, imagine a blood donor fills a 250mL blood bag at 70mL/min on the first visit, and 90mL/min the second visit. What is the average rate at which the donor fills a bag? Let's break it down:

250mL @ 70mL/min = 3.571 mins total

250mL @ 90mL/min = 2.778 mins total

So 500mL total in (3.571+2.778) mins total = 500/6.349 = 78.753 mL/min

So the harmonic mean of 2/[1/70+1/90] = 78.750 gives a more accurate description of average rate, in this example, than the arithmetic mean (80mL/min).

This, however, only applies to rate. If, for example, you wanted to calculate average time to donate it would just be the arithmetic mean (3.571+2.778)/2 = 3.175 mins.