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Worked example: Creating a box plot (odd number of data points)

A box-and-whisker plot is a handy tool for visualizing data. By ordering numbers, we can find the range, median, and quartiles. Practice makes perfect when mastering these concepts!

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Video transcript

- [Voiceover] Represent the following data using a box-and-whiskers plot. Exclude the median when computing the quartiles. Alright, let's see if we can do this. So, we have a bunch of data, here, and they say if it helps, you might drag the numbers to put them in a different order. So, we can drag these numbers around, which is useful, because we will want to order them. The order isn't checked with your answer, and I'm doing this off of the Khan Academy exercises, so I don't have my drawing tablet here. I just have my mouse, and I'm interacting with the exercise, which I encourage you to do too, because the best way to learn any of this stuff is to actually practice it, and at Khan Academy, we have 150,000 exercises for you to practice with. Anyway, so, let's do this. Let's order this thing, so we can figure out the range of numbers. What's the lowest and what's the highest? Let's see, there's a seven here. Then, let's see, we have some eights. We've got some eights goin' on. Then we have some nines, actually we have a bunch of nines, we have four nines here. We have some nines, and then, let's see, 13 is the largest number. There we go, we've ordered the numbers. So, our smallest number is seven, and this is what the whiskers are useful for. For helping us figure out the entire range of numbers. Our smallest number is seven. Our largest number is 13, so we know the range. Now, let's plot the median, and this'll help us once getting this center line of our box, but then also we need to do that, to figure out what these other lines are, that kind of define the box. To define the middle two fourths of our number. Of our data, or the middle two quartiles. Roughly the middle two quartiles, it depends how some of the numbers work out. But this middle line is going to be the median of our entire data set. Now, the median is just the middle number. If we sort them in order, median is just the middle number. We have 11 numbers here. So, the middle one is gonna have five on either side. It's just gonna be this nine. If we had 10 numbers here, if we had an even number of numbers, you actually would of had two middle numbers, and then to find the median, you'd found the mean of those two. If that last sentence was confusing, watch the videos on Khan Academy, on median, and I go into much more detail on that. But here, I have 11 numbers, so my median is going to be the middle one. It has five larger, five less, it's this nine, right over here. If I had my pen tablet, I would circle it. So, it's this nine. That is the median. Now, we need to figure out what number is half way, what number is the median of the numbers in this bottom half? They told us to exclude the median when we compute the quartiles. So, this was the median. Let's ignore that. So, let's look at all of the numbers below that. So, this nine, eight, eight, eight, and seven. So, we have five numbers. What's the median of these five numbers? Well the median's the middle number. That is eight. So, the beginning of our second quartile is gonna be an eight, right over there. We do the same thing for our third quartile. Remember, this was our median of our entire data set. Let's exclude it. Let's look at the top half of the numbers, so to speak. There's five numbers here, in order. So, the middle one, the median of this is 10. So, that's gonna be the top of our second quartile. Just like that, we're done. We have constructed our box-and-whisker plot.