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Classifying shapes of distributions

When we describe shapes of distributions, we commonly use words like symmetric, left-skewed, right-skewed, bimodal, and uniform. Not every distribution fits one of these descriptions, but they are still a useful way to summarize the overall shape of many distributions.

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Video transcript

- [Instructor] What we have here are six different distributions. And what we're gonna do with this video is think about how to classify them, or use the words people typically use to classify distributions. So, let's first look at this distribution right over here, it's the distribution of the lengths of houseflies. So, someone went out there and measured a bunch of houseflies. And then said, "Hey look, there's many houseflies that are between six tenths of a centimeter and six and a half tenths of a centimeter." Looks like there's about 40 houseflies there. And then if you say between six and a half and seven tenths, there's about 30 houseflies. And if you were to say between five and a half tenths and six tenths, it looks like it's about the same amount. This type of distribution is usually described as being symmetric. Why is it called that? Because if you were to draw a line down the middle of this distribution, both sides look like mirror images of each other. This one looks pretty exactly symmetric. But more typically when you're collecting data, you'll see roughly symmetric distributions. Now, here we have a distribution that gives us the dates on pennies. So, someone went out there, observed a bunch of pennies, looked at the dates on them. They saw many pennies, looks like a little bit more than 55 pennies, had a date between 2010 and 2020. While very few pennies had a date older than 1980 on them. And this type of distribution when you have a tail to the left, you can see it right over here, you have a long tail to the left, this is known as a left-skewed distribution. Left-skewed. Now in future videos, we'll come up with more technical definitions of what makes it left-skewed, but the way that you can recognize it is, you have the high points of your distribution on the right, but then you have this long tail that skews it to the left. Now, the other side of a left-skewed, you might say, well, that would be a right-skewed distribution, and that's exactly what we see right over here. This is a distribution of state representatives, and as you can see, most of the states in the United States have between zero and ten representatives. It looks like it's a little over 35. None of them actually have zero, they all have at least one representative, but they would fall into this bucket, while very few have more than 50 representatives. So, here where the bulk of our distribution is to the left, where we have this tail that skews us to the right, this is known as a right-skewed distribution. Now, if we look at this next distribution, what would this be? Pause this video and think about it. Well, this could be a distribution of maybe someone went around the office and surveyed how many cups of coffee each person drank, and if they found someone who drank one cup of coffee per day, maybe this would be them. If they found another person who drinks one cup of coffee, that's them, then they found three people who drank two cups of coffee. Well, this is a very similar situation to what we saw on the dates on pennies. A large amount of our data fell into this right bucket of three cups of coffee, but then we have this tail to the left. So, this would be left-skewed. Now, these right two distributions are interesting. One could argue that this distribution here, which is telling us the number of days that we had different high temperatures, that this looks roughly symmetric, or actually even looks exactly symmetric. 'Cause if you did that little exercise of drawing a dotted line down the middle, it looks like the two sides are mirror images of each other. Now, that would not be technically incorrect. But typically when you see these two peaks, this would typically be called a bi-modal distribution. So, even though bi-modal distributions can sometimes be symmetric or roughly symmetric, you wanna be more precise, and here when you have these two peaks, that's where the bi comes from. You'd call it bi-modal, and this makes sense because you have a lot of days that are warm that might happen during the summer and you might have a lot of days that are cold that are happening during the winter. Now, this last distribution here, the results from die rolls, one could argue as well that this is roughly symmetric. It's not exact, it's not perfectly symmetric, but when you look at this dotted line here on the left and the right sides it looks roughly symmetric. But a more exact classification here would be that it looks approximately uniform. So, rather than calling it a symmetric distribution, or a roughly symmetric distribution, most people would classify this as an approximately uniform distribution.