Furthermore, if there are certain weights associated with each observation then we can calculate the weighted harmonic mean. We first take the sum of the reciprocals of each term in the given data set. Then we divide the total number of terms n in the data set by this value to get the harmonic mean.
When we have a data set, the geometric mean can be determined by taking the n th root of the product of all the n terms. To find the harmonic mean we divide n by the sum of the reciprocals of the terms.
The harmonic mean will always have a lower value than the geometric mean. Harmonic mean is not the reciprocal of the arithmetic mean. Harmonic mean is the reciprocal of the arithmetic mean of the reciprocal terms in a given set of observations.
The harmonic mean has a rigid value and does not get affected by fluctuations in the sample however if the sample contains a zero term we cannot calculate the harmonic mean. Also, the formula to determine the harmonic mean can result in complex computations. Harmonic mean sees widespread use in geometry and music. It is also used to calculate the average of ratios as it equalizes all the data points.
Learn Practice Download. Harmonic Mean Harmonic mean is a type of numerical average that is usually used in situations when the average rate or rate of change needs to be calculated. What is Harmonic Mean? Harmonic Mean Formula 3. How to Find Harmonic Mean? Harmonic Mean vs Arithmetic Mean 6. Merits and Demerits of Harmonic Mean 8. Uses of Harmonic Mean 9. Weighted Harmonic Mean Harmonic mean is a type of average generally used for numbers that represent a rate or ratio such as the precision and the recall in information retrieval.
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. Create a personalised content profile. Measure ad performance.
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Your Practice. Popular Courses. What Is a Harmonic Mean? Harmonic means are used in finance to average data like price multiples.
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?
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