Histograms reveal patterns in data that summary statistics miss. The lecture covers non-normal distributions like bimodal and skewed shapes using examples from illness treatment and wine production, then shows how world population density varies by latitude (normal distribution) versus longitude (peaks at China and India).
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So to summarize this segment, we use histograms to display an entire distribution because they sometimes reveal information that summary statistics gloss over or won't tell us. And many, if not most, distributions that we deal with are going to be normal. But. But some distributions are not normal. For example, we looked at the bimodal distribution with the two classrooms of kids who were sick, the ones who were treated and not treated. We looked at positively skewed distributions, negatively skewed. We looked at uniform distributions. So that was like the white wine distribution in France. That's uniform, or another phrase for that is platykurtic. And the last type that we looked at was leptokurtic. That was like the white wine distribution in Argentina. With that one steep peak is also called a leptokurtic distribution. And now I just wanted to show you a couple of advanced visuals or advanced histograms. And if we could zoom in on these, if you could zoom in on the top and then the bottom. Since we talked about longitude and latitude and we talked about histograms, I wanted to show just these two very cool graphics that I just picked off the Internet. And what this shows is the world population as a function of latitude and as a function of longitude. So if you look at the top graph, what we're plotting is you get this, like, nice normal distribution, pretty much, right? What that means is most people live around the equator, and as you move away from the equator, fewer and fewer people live in those places. The same can't be said about longitude. Right? So if we look at the bottom graph, we don't get a nice normal distribution. Instead, we get like a peak here, a peak here. What are those peaks? Well, here, this peak is probably China. This peak reflects the population in India. Right? So where you have a normal distribution of population around latitude centered around the equator, the same can't be said for longitude. The distribution is not normal. The population distribution is not normal across longitude.
