Harmonic Mean example (Ungrouped data)

Find the Harmonic mean of the following data:

{4, 5, 10, 8, 12, 6, 11}

Step 1: Finding the reciprocal of the values

1/4= 0.25

1/5= 0.2

And so on…

Step 2: Calculate the average of the reciprocal values obtained from step 1.

Here, n is 7.

Average = (0.25 + 0.2 + 0.1 + 0.125 + 0.083 + 0.167 + 0.90)/7

Average = 1.825/7

Step 3: Finally, take the reciprocal of the average value obtained from step 2.

 

Harmonic Mean = 1/ Average
 
Harmonic Mean = 7/1.825
 
Harmonic Mean = 3.836
 
Hence, the harmonic mean for the given data is 3.836.


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