HARMONIC MEAN
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, ... an, 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 number
So, 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, ... an, 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
Quick Summary
- Harmonic Mean is useful for finding averages of rates.
- It is most appropriate when dealing with rates or ratios where the denominator is constant.
🍎 Teacher Insights
Emphasize the application of Harmonic Mean in real-world scenarios involving rates and ratios. Provide examples where it yields a more accurate average compared to the arithmetic mean.🎓 Prerequisites
- Mean
- Reciprocal
- Arithmetic
Check Your Knowledge
Q1: What is the harmonic mean of 2 and 8?
Q2: Calculate the harmonic mean of 15, 30 and 45.
Frequently Asked Questions
Q: When is Harmonic Mean most useful?
A: When dealing with rates or ratios, especially when the denominator is constant (e.g., average speed for the same distance).
Q: How does Harmonic Mean differ from Arithmetic Mean?
A: Arithmetic Mean is the sum of the numbers divided by the count, while Harmonic Mean involves the reciprocals of the numbers.