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
External links
- Medical encyclopedia article on Harmonic mean
- Wikipedia's article - Harmonic mean
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