DEFINITION of 'Harmonic Mean'
The harmonic mean is an average. It is calculated by dividing the number of observations by the reciprocal of each number in the series. Thus, the harmonic mean is the reciprocal of the arithmetic mean of the reciprocals.
The harmonic mean of 1,4, and 4 is:
BREAKING DOWN 'Harmonic Mean'
The weighted harmonic mean is used in finance to average multiples like the priceearnings ratio, because it gives equal weight to each data point. Using a weighted arithmetic mean to average these ratios would give greater weight to high data points than low data points, because priceearnings ratios aren't pricenormalized while the earnings are equalized.
The harmonic mean is the weighted harmonic mean, where the weights are equal to 1. The weighted harmonic mean of x_{1}, x_{2}, x_{3} with the corresponding weights w_{1}, w_{2}, w_{3} is given as:
As an example, take two firms. One has a market capitalization of $100 billion and earnings of $4 billion (P/E of 25) and one with a market capitalization of $1 billion and earnings of $4 million (P/E of 250). In an index made of the two stocks, with 10% invested in the first and 90% invested in the second, the P/E ratio of the index is:
Using the weighted arithmetic mean: P/E = 0.1x25 + 0.9x 250 = 227.5
Using the weighted harmonic mean: P/E = (0.1 + 0.9) / (0.1/25 + 0.9/250) ≈ 131.6
As can be seen, the weighted arithmetic mean significantly overestimates the mean priceearnings ratio.

Arithmetic Mean
Arithmetic mean is the sum of all the numbers in the series divided ... 
Arithmetic Index
Arithmetic index uses an arithmetic sum to determine changes ... 
Weighted
Weighted is a description of adjustments to a figure to account ... 
PriceEarnings Relative
The priceearnings relative figure is the priceearnings ratio ... 
PriceEarnings Ratio  P/E Ratio
The PricetoEarnings Ratio or P/E ratio is a ratio for valuing ... 
NASDAQ100 Equal Weighted Index
The NASDAQ100 Equal Weighted Index is an equalweighted version ...

Investing
Breaking Down The Geometric Mean
Understanding portfolio performance, whether for a selfmanaged, discretionary portfolio or a nondiscretionary portfolio, is vital to determining whether the portfolio strategy is working or ... 
Investing
Investigating the Effectiveness of EqualWeight ETFs
Investors should know the ins and outs of equally weighting stocks before considering the related ETFs. 
Investing
How Do I Calculate the PriceEarnings Ratio?
If Apple is trading at $108.73 per share, and its trailing twelve months' EPS is $6.45, calculate the P/E ratio as... 
Investing
3 Types Of Indexing For ETF Success
ETF success relies on the index with which it's paired. Discover three index genres for tracking average market performance. 
Trading
How To Make The Most of Fibonacci Grids (VDSI, GLW)
Build your Fibonacci skills by finding the longest price swing on your chart of interest and placing a grid over the trend. Repeat at shorter intervals. 
Investing
Can Investors Trust The P/E Ratio?
The P/E ratio is one of the most popular stock market ratios, but it has some serious flaws that investors should know about. 
Investing
Time to Sell Weight Watchers After 103% YeartoDate Gain?
Shares of Weight Watchers surged as a successful turnaround gained momentum. Is there more room to run? 
Investing
Sysco and Other Big Movers In Services
The market has been slipping so far today. The Nasdaq has fallen 0.3%; the S&P 500 has fallen 0.4%; and the Dow has declined 0.5%. The Services sector (IYC) is currently lagging behind the overall ...

What is the average pricetoearnings ratio in the banking sector?
Explore the price/earnings ratio in regard to the banking industry and learn what the average P/E ratio is for most banking ... Read Answer >> 
How do I use Excel to calculate a weighted average?
Learn about the calculation and interpretation of weighted averages, including how to compute a weighted average using Microsoft ... Read Answer >> 
How can the pricetoearnings (P/E) ratio mislead investors?
A low P/E ratio doesn't automatically mean a stock is undervalued, just like a high P/E ratio doesn't necessarily mean it ... Read Answer >>