Harmonic Mean

The harmonic mean is a measure of central tendency that is calculated by taking the reciprocal of the average of the reciprocals of a set of numbers. It is often used to find the average of a set of numbers that have very different values.

Formula:

The harmonic mean (Hm) of a set of numbers is given by the formula:

Hm = n(a1, a2, ..., an) / (n-1)

where:

• Hm is the harmonic mean
• n is the number of numbers in the set
• a1, a2, …, an are the numbers in the set

Example:

The harmonic mean of the numbers 2, 4, and 6 is:

Hm = 3(2, 4, 6) = 3

This is because the reciprocal of each number is 1/2, 1/4, and 1/6, respectively. The average of these reciprocals is 1/3, so the harmonic mean of the numbers 2, 4, and 6 is 3.

Advantages:

• The harmonic mean is resistant to outliers, meaning that it is not affected by extreme values.
• The harmonic mean is a good measure of central tendency for data that has a wide range of values.
• The harmonic mean can be used to compare multiple sets of numbers.

Disadvantages:

• The harmonic mean can be difficult to calculate for large sets of numbers.
• The harmonic mean can be misleading if the data is not evenly distributed.
• The harmonic mean can be biased, meaning that it can favor certain values over others.