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Usually, the average value we use is the average value obtained by adding all the data such as “average age,” “average height,” “average weight,” and dividing by the number of data (number of people). This is referred to as the “arithmetic average.”
Earlier, we explained the “Geometric average.” So, what kind of average is the “harmonic average”? In this study, we will explain the harmonic average.
Harmonic average
The harmonic average is the arithmetic average obtained by taking the reciprocal of each data point for n data points.
Harmonic averages are often used when the reciprocal of the data is meaningful. The meaning of the reciprocal is, for example, “speed x = 30 km/hour” when traveling a certain distance, the reciprocal is “1/x = 1/30”.
This is “the time it took to go one kilometer” and, therefore, “the reciprocal is meaningful.”
Formula for calculating the harmonic average
[Formula]
When n data are X1 , X2 , X3・・・Xn ,
※However, except where the data contains 0 and negative values.
Find the harmonic average of speed.
Let each speed be X1 , X2 , and X3, and substitute them into the above formula.
Therefore, the harmonic average is 20 km/h.
Notes on harmonic average
In the above example, the total 180 km was run in 9 hours, so the average is considered to be 180 km÷9 = 20 km/hour. This is the concept of harmonic average.
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