Why Harmonic Mean is used to calculate F1-Measure?

In this post, we will discuss why do we use Harmonic Mean to calculate F1 score and what is the intuition behind this? and why can’t we just use the product of precision and recall that would also give us a metric that would combine the result of precision and recall? Also, the range of this metric will be in the range of 0 to 1, as both precision and recall lie between 0 and 1, hence the product. By the end of this blog, I will answer all these questions.

F1 score gif with recall and precision
src: https://pmirla.github.io/assets/harmonic_mean.gif