Screencast 4 Interpreting a boxplot

Transcript

INSTRUCTOR
In this screencast, I’m going to talk about interpreting a boxplot. And what we have here is an example of a boxplot. And it happens to be Figure 18 from Subsection 3.3 of Unit 2. And it’s a boxplot of the small television prices. And you can see here that television prices are given in pounds, and they go from just under £100 up to £275.
The first thing on the boxplot to look at is the box itself – in particular, to look at the ends of the box. The end on the left hand side shows us where the lower quartile is. And here is about £130. The end on the right hand side shows us where the upper quartile is – Q3. And this translates to about £180. So the lower quartile is about £130, and the upper quartile is about £180.
The line in the middle of the box shows us where the median is. And this is about £150. So the price of the median small television is £150. Notice in this example, it is quite clear where the line is in the middle of the box. There are some examples where the median is the same as the lower quartile or where the median is the same as the upper quartile. And then you won’t actually see a line in the box. The line will be at one end or the other.
The other thing to notice on the boxplot are the two whiskers. So there’s a whisker on the right hand side and a whisker on the left hand side. The whisker on the right hand side shows us where the values that are high but not too high are. Similarly, on the left hand side, the whisker on the left hand side shows us where the values are low but not too low are.
And finally, notice there’s one point here marked all by itself. And this is a value that we wonder whether it’s too high. In other words, we’re marking this one out as a potential outlier. This shows all the elements that are on a boxplot. And one thing we can use these elements for is to say something about the symmetry of the data.
And one thing we can look at is where the median is relative to the two ends of the box. So here we notice that the left hand side is short relative to the right hand side. We can look at the whiskers in the same way, and notice that the whisker on the left hand side is relatively short. And the whisker on the right hand side is relatively long.
And both these observations together suggest that the data are right-skew. The data tends to be more spread out on the right hand side of the median relative to the data on the left hand side the median. And notice, in doing this, we haven’t actually taken account of the outlier. If we took the outlier into account as well, this would only emphasise more that the data are right-skew. Because this adds to the impression that the data are more spread out to the right of the median relative to the left of the median.

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