Normal Distributions

Publish Date
Principles Series
Last Edit
Apr 3, 2022 01:48 PM
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It’s been said before, but reading the news is a painful act for any statistician or mathematician. With an education system that butchers math education, and journalists most likely to be those who gravitate more towards words, this is hardly a surprise.
Why is this such a problem? Math unveils the truth more effectively than almost any other tool we have at our disposal. In our alleged “post-truth” era, math is one of our best assets to avoid getting sucked into ridiculous views or debates.
A necessary aside: one of the main ways that our educational system is behind is that it emphasizes trigonometry and calculus over statistics. Circa-2019, this is criminal. Let me put it this way: if you are a parent, don’t wait for the schools. Start teaching your kids basic statistics around 4th or 5th grade. You can thank me later.
Anyway, we’re not going to give a full statistics lesson here (at least not yet!), but a few concepts should be potable and relevant. One of those is the normal distribution. The normal distribution is beautiful and among the most universal concepts out there. If you ever come across a postmodernist misguided enough to suggest that math is a social construct, simply ask them to go out and measure the petal length of 1,000 flowers and report back their findings.
The above exercise would undoubtedly yield a normal distribution, because almost everything we find in nature is normally distributed. Indeed, the above exercise has been done, and the results will always look something like this:
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Mathematically, this is defined by explicit terms used heavily within statistics. We won’t get into that here, but the standard normal distribution looks like this:
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This isn’t magic, even if it can sometimes feel like it. Here’s a fun example below: my weekly step count over the past 3.5 years. This is normally distributed! And it’d be pretty damn hard for me to avoid that even if I tried.
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What else follows normal distributions? Pretty much any measurement of humans, animals, or plants: height, weight, arm length, et cetera. Is that not enough? Well most things that are aggregations will end up being normal as well, as was the case with my weekly step count, but it is just as true for the daily or weekly number of visitors to a restaurant, website, and more (though both of these would have long-tailed outliers when there’s a festival nearby or a post goes viral). When in doubt, a good guess is that something is going to be normally distributed.
Why does this matter? There are many implications, but so far as the news is concerned: most of it is written without concern for the implications of a distribution. They speak in terms of averages, anecdotes, and absolutes. Such basic tools tell good stories but are absolute rubbish when it comes to uncovering the truth. This leads to the spread of bad ideas and misconceptions that poison public discourse. Do your part and learn some statistics!