Explain the use of harmonic mean as an average. Given the following frequency distribution of first year students of a particular college, calculate the harmonic mean.
Age 13 14 15 16 17No. of students 2 5 13 7 3
4.
No. of students 2 5 13 7 3
No. of students 2 5 13 7 3
Explanation
The harmonic mean is a type of average used to find the reciprocal of the arithmetic mean of reciprocals. It's particularly useful when dealing with rates, ratios, or other situations where extreme values need to be balanced out. The formula for the harmonic mean for a set of n data points, x1, x2, ..., xn, is:
Harmonic Mean (H) = n / [(1/x1) + (1/x2) + ... + (1/xn)]
In this case, you have a frequency distribution of ages and the number of students for each age group. To calculate the harmonic mean
1. Reciprocals:
- 1/13 = 0.0769 (for 13-year-olds)
- 1/14