The harmonic mean calculates the average of rates or ratios. You calculate it by dividing the number of observations by the sum of the reciprocals of the values. The harmonic mean gives less weight to large values and is especially useful when averaging quantities like speeds, prices, or other rates over equal distances or tasks.
For example, if you drive 60 miles at 30 mph and another 60 miles at 60 mph, the harmonic mean gives the correct average speed over the whole trip. This is better than using the simple average, which would incorrectly suggest 45 mph.
The harmonic mean formula is as follows for two values (n = 2), x1 and x2:
Harmonic mean = n / (1/x₁ + 1/x₂)
Substitute the known values:
Harmonic mean = 2 / (1/30 + 1/60)
First, calculate the reciprocals:
1/30 ≈ 0.0333, 1/60 ≈ 0.0167
Now, sum the reciprocals:
0.0333 + 0.0167 = 0.05
Finally, divide:
2 / 0.05 = 40
So, the harmonic mean speed is 40 mph.
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