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## Box and whisker plots

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

AP.STATS:

UNC‑1 (EU)

, UNC‑1.L (LO)

, UNC‑1.L.1 (EK)

, UNC‑1.L.2 (EK)

CCSS.Math: , ## 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.