httpness: (studying statistics) Can there be a different standard deviation up and down?

isomorphisms: Yes. it’s called a semideviation. (Or a quasinorm.) There are a lot of people who argue that semideviations and quasinorms are more natural than standard deviation and norms.

httpness: So that’s not a normal distribution?

isomorphisms: Whatever distribution you’re using, there are different measures of dispersion on that — standard deviation, downside risk / semideviation, interquartile range, kurtosis, etc.

httpness: I was just thinking about temperatures. The standard deviation changes depending on the time of year, and the chance of unseasonably warm or cold days changes too.

httpness: Here’s an example of what I mean. let’s say during the summer there _is_ a standard deviation and it’s the same up and down. But at another time of year there could be more chance of a very warm day, and at a third time of year there could be more chance of an unseasonably cold day.

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Tags: abstract algebra, assumption of constant variance, assumptions, beginner's mind, constant variance, directionality, dispersion, Gaussian, Gaussian distribution, homoscedasticity, homoskedasticity, interquartile range, IQR, kurtosis, math, mathematics, maths, moments, normal distribution, probability distribution, quasinorms, semideviation, statistics, summer, teaching, temperature, weather

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