Harmonic Mean

The harmonic mean is:

the reciprocal of the arithmetic mean of the reciprocals

Yes, that is a lot of reciprocals!

("Reciprocal" just means 1value)

The formula is:

Harmonic Mean

Where a,b,c,... are the values, and n is how many values.


Example: What is the harmonic mean of 1, 2 and 4?

The reciprocals of 1, 2 and 4 are:

11 = 1,   12 = 0.5,   14 = 0.25

Now add them up:

1 + 0.5 + 0.25 = 1.75

Divide by how many:

Average = 1.753

The reciprocal of that average is our answer:

Harmonic Mean = 31.75 = 1.714 (to 3 places)

Another way to think of it

We can rearrange the formula above to look like this:

Harmonic Mean

It is not easy to use this way, but it does look more "balanced" (n on one side matched with n 1s on the other, and the mean matched with the values too).