The harmonic mean of a set of observations is the reciprocal of the arithmetic mean of the reciprocal of the observations. Harmonic mean is defined only for non-zero positive values and is used for averaging while keeping one variable constant. For example in first test a typist types 400 words in 50 minutes, in second test he types the same words (400) in 40 minutes and in third test he takes 30 minutes to type the 400 words. Determine his average speed for the three tests. (Note here constant variable is 400 words).

Therefore,

The calculation of H.M for the ungrouped data is slightly different from that of grouped data. Calculations for both types of data are given below.

### Harmonic Mean of Ungrouped Data

In order to calculate the harmonic mean of ungrouped data the formula will be:

Here,

N is the total number of observations

And x represents the values of observations while ?1/x shows the sum of reciprocal of observations.

**Problem:** During one month the total number of kilometers driven by each truck is given below. Find the geometric mean.

### Harmonic Mean of grouped Data

Harmonic mean of grouped data can be calculated with the help of following formula:

Here,

N is the sum of all frequencies

f is the frequency corresponding to each observation x while ?f/x represents the sum of reciprocal of grouped observations.

**Problem:** Following is the frequency distribution of the marks (out of 40) obtained by the students of a certain college in statistics. Calculate harmonic mean.

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