Why is harmonic mean used

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These choices will be signaled globally to our partners and will not affect browsing data. We and our partners process data to: Actively scan device characteristics for identification. I Accept Show Purposes. Your Money. Personal Finance. Your Practice. Popular Courses. What Is a Harmonic Mean? Harmonic means are used in finance to average data like price multiples.

Harmonic means can also be used by market technicians to identify patterns such as Fibonacci sequences. Compare Accounts. The offers that appear in this table are from partnerships from which Investopedia receives compensation. This compensation may impact how and where listings appear. Investopedia does not include all offers available in the marketplace. The harmonic mean can be described as the reciprocal of the arithmetic mean of the reciprocals of the data.

This can be expressed mathematically as. H is the harmonic mean, n is the number of data points in the set, is the nth value in the data set. The harmonic mean is the smaller of the three Pythagorean means and tends to emphasize the impact of small outliers while minimizing the impact of large outliers.

When dealing with rates, the harmonic mean is considered to be the true average compared to the arithmetic average and this can easily be proven by calculating average speed. Assume a vehicle travels 10 miles at 60 mph this would take 10 minutes and then travels another 10 miles at 30 mph this would take 20 minutes.

It is least affected by fluctuation in sampling. It gives to greater importance to small items. It is capable of further algebraic treatment. It is difficult to calculate. It does not give equal weight to every item. It may not be represented in the actual data. It is not defined for negative value. Steps to Calculate Harmonic Mean. Step 2: Find the average of those reciprocals, by just adding them and divide by number of total values.

Step 3: Then do the reciprocal of that average. Solve Example. What is the harmonic mean of 4, 5 and 10? The reciprocals of 4, 5 and 10 are:. Now add them. Total values are 3 so divide it by 3. The reciprocal of that average is our answer:.