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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!

## Want to join the conversation?

- can you give me some practice problems? what happened to those?(11 votes)
- Here to practice how to make them:

https://www.khanacademy.org/math/ap-statistics/summarizing-quantitative-data-ap/stats-box-whisker-plots/e/box-plots

Here is how to practice how to read them:

https://www.khanacademy.org/math/ap-statistics/summarizing-quantitative-data-ap/stats-box-whisker-plots/e/analyzing-data-with-box-plots(12 votes)

- I still don't really understand how to create box plots. Can someone help me understand please.(5 votes)
- 1) Order numbers from least to greatest

2) Find median, if there is an even number of values take the mean of the middle 2

3) Q1 is the middle value between median and lowest value. If there is an even number of values in between median and lowest value, then take mean of the middle 2. Do the same with the upper half to find Q3.

4) Draw it out over a number line(10 votes)

- cant understand what exclude the median means(4 votes)
- When you calculate the 1st and 3rd quartile values, count after the median to the endpoint.

In the even number example, you start counting all the numbers in each half which includes 7 numbers for this example. So you find the middle of that grouping.

in the odd number of objects example, the median is an actual number. When counting out the quartile, you ignore that one(4 votes)

- Whatever happened to the exercise shown is the video? It looks great practice for this skill!(4 votes)
- Why do you show examples before defining what is being explained?

You jump right into a box-and-whisker plot example without even a brief explanation of what the box-and-whisker plot is.

Having watched the example, it is a simple concept and the example was enough to explain it - still a brief summary before launching into an example would be nice.(4 votes) - Thanks for the help(3 votes)
- Suggestion regarding meaning of words, such as "top of Q1" could also be called "beginning of Q2." This has been confusing me when you say Q3 minus Q1. Please say what is range from beingging of Q2 to end of Q3. Don't use "top of" use beginning of"(3 votes)
- I am not sure I have understood your question.

Q3 is the 75th percentile and Q1 is 25th percentile. Basically you take the median and then take media again.

We could regard the beginning of the 2nd quartile as the top of quartile 1. As both these are the 25th percentile. I guess it is matter of preference.

Basically Q1, Q2 and Q3 are already defined. But each quartile represents 25% of the data. So they are different concepts.(1 vote)

- I'm confused, isn't it standard not to include the median in the IQR unless the number of data points is even? Why does it say not to include the median in the IQR in the exercise if that is standard procedure (in this case)?(2 votes)
- It's just a reminder.(2 votes)

- What is a mean?(1 vote)
- The average of all numbers, to find it, add all of the numbers and then divide by how many numbers there are.(2 votes)

- what is 100/1(0 votes)

## 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.