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HARMONIC MEAN (H.M.)

The reciprocal of the H.M. of a variate is the A.M. of its reciprocal.

For the observations      x1, x2, ….., x 

For grouped frequency distribution xi is taken as class mark. 

Note. A.M. G.M.  H.M.

Example 3. Suppose a train moves 100 km with a speed of 40 k/lhr. then 150 km with a speed of 50 km/hr and next 135 km with a speed of 45 km/hr. Calculate the average speed. 

Solution. To get average speed we require harmonic mean of 40,50 and 45 with 100, 150 and 135 as the respective frequency or weights.

Hence the average speed per hour is 45.29 km.

 

Note. In the case of grouped frequency distributions with open end class at one extremity or at both the extremities, the A.M., G.M. and H.M. cannot be computed unless we make some plausible assumptions.