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I'm spreadsheeting my favorite albums and I'd like the good tracks on the album to count more for its average than the bad songs. I thought about geometric means, but those do the opposite of what I want.

Is my best course of action to raise each value to a certain number and then sum them and divide by some constant?

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  • $\begingroup$ Yeah, you could choose some $\alpha>1$ and then calculate the quantity $$ \left(\frac{1}{N} \sum_i x_i^{\alpha} \right)^{1/\alpha} $$ where $x_i$ are the values. $\endgroup$
    – Matti P.
    Nov 26, 2019 at 8:35

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The generalized $p$-mean will do roughly what you want:

$$A_p = \left(\frac{1}{N}\sum_{i=1}^N x_i^p\right)^{1/p}.$$

When $p=1$, you get the usual mean. The large $p$ you choose, the more the outliers will dominate the average (so that as $p\to\infty$, the album average approaches the maximum of the song scores.)

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