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[Editor’s note: I never got around to completing this post, but this post I just read about how the sound of popcorn being popped is the sound of the normal distribution seemed like a worthy addition to this post.]

Many everyday problems that involve statistics require making many observations about something quantifiable and being able to figure out the most probable value of that observation. For example, maybe you’re trying to figure out what mileage your car’s giving you, so every time you fill the tank up, you record how many miles you go before you empty it out. You might ask, what is the average distance my car will go on a full tank?

One way to solve this problem is to take an average of all your observations. The simple average is not a very good statistical measure, mainly because it’s influenced by “outliers.” If one of the observations you took of how many miles you went on a full tank of gas involved a very long highway road trip, then the average measure will make it look like you get really awesome mileage. That’s why car companies have to report a highway and a city mileage – the average highway mileage is bound to be higher than the average city-only mileage, and taking an average that combines the two would be misleading.

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