PROBLEMS ON HARMONIC MEAN

Example 1 :

Find the H of 3, 4,  5,  6, 7 and 8

Solution :

The total number of values  =  6

Let us find H using the formula

H  =  n /(1/a₁ + 1/a₂ +.....+1/aₓ)

=  6/(1/3+1/4+1/5+1/6+1/7+1/8)

=  6/(0.333+0.25+0.20+0.166+0.142+0.125)

=  6/1.216

=  4.93

Example 2 :

Find the H of 1, 2, 5, 7, 9

Solution :

The total number of values = 5

Let us find H using the formula

H  =  n /(1/a₁ + 1/a₂ +.....+1/aₓ)

=  6/(1/1+1/2+1/5+1/7+1/9)

=  6/(1 + 0.5 + 0.2 + 0. 14 + 0.11)

=  6/1.95

=  3.07

Harmonic mean of two numbers

Example 1 :

Find the H of two numbers 50 and 30.

Solution :

Instead of x₁ and x₂ we are having 50 and 30.

=  2(50) (30) / (50 + 30 )

=  (100 x 30)/80      

=  3000/80

=  37.5

Example 2 :

Find the H of two numbers 12 and 15.

Solution :

Instead of x₁ and x₂ we are having 12 and 15.

=  2(12) (15) / (12 + 15 )

=  (24 x 15)/27

=  360/27

=  13.3

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