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## Box and whisker plots

Current time:0:00Total duration:3:15

# Worked example: Creating a box plot (even 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: 6.SP.B.4

## Video transcript

- [Voiceover] Represent the following data using a box-and-whiskers plot. Once again, exclude the median
when computing the quartiles. And they gave us a bunch of data points, and it says, if it helps, you
might drag the numbers around, which I will do, because
that will be useful. And they say the order isn't checked, and that's because I'm doing
this on Khan Academy exercises. Up here in the top right,
where you can't see, there's actually a check answer. So I encourage you to use
the exercises yourself, but let's just use this as an example. So the first thing, if I'm
going to do a box-and-whiskers, I'm going to order these numbers. So let me order these numbers
from least to greatest. So let's see. There's a one here, and
we've got some twos. We've got some twos here and some threes, some threes, some four-- I have one four and fives. I have a six. I have a seven. I have a couple of
eights, and I have a 10. So there you go. I have ordered these numbers
from least to greatest, and now, well just like that,
I can plot the whiskers, because I see the range. My lowest number is one. So my lowest number is one. My largest number is 10. So the whiskers help
me visualize the range. Now let me think about the
median of my data set is. So my median here is
going to be, let's see. I have one, two, three,
four, five, six, seven, eight, nine, 10, 11, 12, 13, 14 numbers. Since I have an even number of numbers, the middle two numbers are
going to help define my median, because there's no one middle number. I might say this number
right over here, this four, but notice, there's one, two, three, four, five, six, seven above it, and there's only one, two,
three, four, five, six below it. Same thing would have
been true for this five. So this four and five, the middle is actually
in between these two. So when you have an even
number of numbers like this, you take the middle two numbers,
this four and this five, and you take the mean of the two. So the mean of four and five
is going to be four-and-a-half. So that's going to be the
median of our entire data set, four-and-a-half, four-and-a-half. And now, I want to figure out the median of the bottom half of numbers
and the top half of numbers. And here they say exclude the median. Of course I'm going to exclude the median. It's not even included in
our data points right here, because our median is 4.5. So now let's take this
bottom half of numbers. Let's take this bottom half
of numbers right over here and find the middle. So this is the bottom seven numbers. And so the median of those is going to be the one which has three on either side, so it's going to be this
two right over here. So that right over there is kind of the left boundary of our box, and then for the right boundary, we need to figure out the middle
of our top half of numbers. Remember, four and five
were our middle two numbers. Our median is right in
between at four-and-a-half. So our top half of numbers
starts at this five and goes to this 10. Seven numbers. The middle one's going to
have three on both sides. The seven has three to the left, remember of the top half, and three to the right. And so the seven is, I guess you could say the
right side of our box. And we're done. We've constructed our
box-and-whiskers plot, which helps us visualize the entire range but also you could say the middle, roughly the middle half of our numbers.

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