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## Get ready for AP® Statistics

# 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: , Learn how to create a box plot. The data set used in this example has 14 data points.

## Want to join the conversation?

- can i get some help what does IQR mean(7 votes)
- The interquartile range. Where you subtract Quartile 3 and Quartile 1.(8 votes)

- I'm confused. In the last worked example when we had an odd number of data, we were taught to eliminate the mean when calculating the upper and lower means. Does that rule not apply with even numbers of data? That was not clear.(2 votes)
- We want the median to divide the data set into two equal halves.

However, with an odd number of data points the two halves can't be equal in size which is why we remove the median before we calculate the upper and lower quartiles.

With an even number of data points we don't have this problem and don't have to remove the median.(3 votes)

- How do I get a profile photo?(2 votes)
- Hang on. This is an off-topic question, so if it doesn't have anything to do with the subject (box + whisker plots), then you can just search for it in the search box at the top of the page. You get a profile photo by tapping the picture on the left of your bio on the "edit profile" section.(2 votes)

- sleep ideas or can you give me some(3 votes)
- I'm not really sure about the next worksheet. Can someone help me?(2 votes)
- what does iqr mean:)(2 votes)
- When working out the median of the first and second half, why did Sal include the 4 and 5?(1 vote)
- The amount of data points that are less than the median is always equal to the amount of data points that are greater than the median.

In this case we have an even number of data points, namely 14 of them, and so the median should be somewhere between the 7th and 8th data points (i.e. between 4 and 5).

We arrange this by letting the median be the mean of those two data points ((4 + 5)∕2 = 4.5).

– – –

When working out the lower quartile we use the same logic, but for the data points up to and not including the median (i.e. all the data points less than 4.5, which does include 4).

Similarly, for the upper quartile we consider the data points above the median (greater than 4.5, thus including 5).(3 votes)

- I dont know how to create a box plot from a histogram. Help please!(2 votes)
- 1. Write out the data for example 1,2,3,3,3,4,5,5,5,5,6,7,8,8,9,9.

2. Put it in a box plot like shown in the video.

Hope this helps.(1 vote)

- what does iqr mean(1 vote)
- How do recreate a histogram from a box and whiskers plot?(1 vote)

## 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.