Harmonic mean

Harmonic Mean

The Harmonic Mean (pronounced: /hɑːrˈmɒnɪk miːn/) is a type of average that is often used in the field of statistics and in various branches of science, including medicine. It is particularly useful in situations where rates or ratios are more important than raw numbers.

Etymology

The term "Harmonic Mean" comes from the field of mathematics, specifically from the branch known as harmonic analysis. The term "harmonic" is derived from the Greek word 'harmonia', which means "a fitting together". The term "mean" is derived from the Middle English word 'mēne', which means "middle" or "intermediate".

Definition

The Harmonic Mean of a set of numbers is the reciprocal of the arithmetic mean of the reciprocals of the numbers. In other words, if you have a set of numbers, you take the reciprocal of each number, add those up, take the arithmetic mean of those numbers, and then take the reciprocal of that result.

Formula

The formula for the Harmonic Mean (HM) is:

HM = n / (1/x1 + 1/x2 + ... + 1/xn)

where:

• n is the total number of values
• x1, x2, ..., xn are the individual values

Use in Medicine

In medicine, the Harmonic Mean is often used in the analysis of biostatistics data. For example, it can be used to calculate the average rate of patient recovery, or the average rate of disease progression.

Related Terms

• Arithmetic Mean
• Geometric Mean
• Median
• Mode
• Range
• Standard Deviation

External links

• Medical encyclopedia article on Harmonic mean
• Wikipedia's article - Harmonic mean

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