|Lecture -10| Concept of Harmonic Means| Sequence and Series| Formula Foundation|

As you may remember, the reciprocal of a number n is simply 1 / n. (e.g. the reciprocal of 5 is 1/5). For numbers that are already fractions, this means that you can simply “flip” the numerator & denominator: reciprocal of 4/5 = 5/4. This is true because 1 divided by a fraction yields that fraction’s reciprocal, e.g. 1 ÷ (4/5) = 5/4.
Another way to think about reciprocals is: two numbers that equal 1 when multiplied together. So when finding the reciprocal of a number n, we are simply asking: what number must we multiply with n in order to get 1. (This is why the reciprocal is also sometimes called the multiplicative inverse.)
So then, the harmonic mean can be described in words as: the reciprocal of the arithmetic mean of the reciprocals of the data set.
Thats a lot of reciprocal flips there, but it’s actually just a few simple steps:
1. Take the reciprocal of all numbers in the data set
2. Find the arithmetic mean of those reciprocals
3. Take the reciprocal of that number

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