What is the harmonic mean?

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The harmonic mean has been causing a stir in the r/datascience subreddit recently. In this video I explain what the harmonic mean is and when it is appropriate to use it. I then work through the job interview question from Reddit, solving it first with a numeric approach, then with the harmonic mean.

Question: "You travelled half of the distance with a speed 30km/h, and the other half - 50km/h. What is the average speed?

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Really useful! Helped with my CFA level 1 exam

therandomizedassasin
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Harmonic mean is how mathematicians do diss tracks.

Madosatoshist
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There is another useful case for it.
You can compute the 'virtual' musical perfect 4th of two notes. If i take the HM of C3 and C4 for example, i get F3. Coincidentally (maybe not?), i get G3 (the perfect 5th) if i take the HM of C3 and C5. 🤔

Gtr
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Another useful case for it is an evaluation metric in machine learning called f1_score

aaryankatoch
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Very clear video! I do have one question though: why exactly does this work? Is the harmonic mean always equal to the arithmetic mean after factoring in ratios? And does that work for any ratios or is this a specific case where it happens to give the same answer?

NilsKimman