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Harmonic Mean PDF Print E-mail
Written by Wilfred Ling   
Monday, 17 November 2008

H = \frac{n}{\frac{1}{x_1} + \frac{1}{x_2} + \cdots + \frac{1}{x_n}} = \frac{n}{\sum_{i=1}^n 1/x_i}, \qquad x_i > 0 \text{ for all } i.

We have heard about mean and geometric mean. But have you heard of harmonic mean? It is more popularly used than the application of mean. How to use harmonic mean? Most people use the idea of harmonic mean without knowing it. It is often used in regular saving plan. Take for example, if you RSP $1000 per month, your average price purchase is the harmonic mean. Here are some examples:

Say on Jan, you RSP $1000 to a unit trust priced at 0.90
On Feb, you RSP $1000 to a unit trust priced at 0.80.

The average price is
= total cost of investment / total number of units bought
= ($1000 + $1000) / ($1000/0.90 + $1000/0.80)
= 2 / ( 1/0.90 + 1/0.80)

Which is the harmonic mean formula.

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