Q: When we calculate the F-Measure considering both Precision and Recall, we take the harmonic mean of the two measures instead of a simple arithmetic mean.
What is the intuitive reason behind taking the harmonic mean and not a simple average?
The harmonic mean is the equivalent of the arithmetic mean for reciprocals of quantities that should be averaged by the arithmetic mean. More precisely, with the harmonic mean, you transform all your numbers to the "averageable" form (by taking the reciprocal), you take their arithmetic mean and then transform the result back to the original representation (by taking the reciprocal again).