Definition Of Harmonic Mean

Harmonic Mean of a set of numbers is the number of items divided by the sum of the reciprocals of the numbers. Hence, the Harmonic Mean of a set of n numbers i.e. a₁, a₂, a₃, ... a_n, is given as

More About Harmonic Mean

In a geometric figure, height is also called as altitude.

Video Examples: Acute and Obtuse Angles in Geometry
 

Example of Harmonic Mean

Let's find the harmonic mean for the numbers 3 and 4.
Sum of the reciprocals of the numberSo, harmonic mean

• = 

Solved Example on Harmonic Mean

Ques: Find the harmonic mean of 15, 30, and 45.

Choices:

A. 55.24
B. 10.22
C. 24.55
D. 16.81
Correct Answer: C

 

Solution:

Step 1: Harmonic Mean of a set of number is the number of items divided by the sum of the reciprocals of the numbers. Harmonic Mean of a set of n numbers i.e. a₁, a₂, a₃, ... a_n, is given as 
Step 2: Harmonic mean = = [Add the reciprocals of the numbers 15, 30, and 45 and divide the sum by 3, as there are three numbers.]
Step 3: =270/11 = 24.55
Step 4: So, the harmonic mean of the numbers 15, 30, and 45 is 24.55. 

Related Terms for Harmonic Mean

Sum
Number
Reciprocal

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