# Box plots. How to draw a box plot from a list of data values (with no outliers)

To be able to draw a box plot you will need 5 values; the lowest value, the lower quartile (LQ), the median, the upper quartile (UQ) and the highest value. If you have a list of numbers then you will need to calculate these values before you can draw the box plot. Make sure the numbers are ordered from smallest to largest before you start.

If you have n values in your list then to find the lower quartile work out ¼ of n. If you get a decimal then round this number up and count along your data values until you reach this number. If you get a whole number then the LQ will be situated between this number and the next along your list of data values.

To calculate the median find ½ of n. If you get a decimal then round this number up and count along your data values until you reach this number. If you get a whole number then the median will be situated between this number and the next along your data values.

To calculate the UQ work out ¾ of n. If you get a decimal then round this number up and count along your data values until you reach this number. If you get a whole number then the UQ will be situated between this number and the next along your data values.

Let’s take a look at an example:

A group of 10 students take a geography test. Their results are:

54%, 68%, 87%, 24%, 39%, 59%, 61%, 89%, 17%, 32%

Draw a box plot to represent their test scores.

First you need to sort the numbers in size order (starting with the smallest value):

17%, 24%, 32%, 39%, 54%, 59%, 61%, 68%, 87%, 89%

Now calculate the 5 values you need for your box plot:

The lowest value is 17% (the first value in the list)

The lower quartile is ¼ of 10 = 2.5 = 3 (round up). So count three numbers in which gives LQ = 24%

The median is ½ of 10 = 5. So the median is between the 5^{th} and 6^{th} value = 57.5%

The upper quartile is at ¾ of 10 = 7.5 = 8 (round up) So count eight numbers in which gives UQ = 68%

The highest value is 89% (the last value in the list)

All you need to do now is draw a horizontal axis for the test scores. Go from 0% to 100%. All you need to do know is mark these five values above the axis. Make a box with the LQ, median and UQ and have 2 horizontal lines coming out from the LQ and UQ to the lowest and highest values on the box plot.

Sometime outliers can be marked on the box plot as well. But you will only have to do this if you are studying a higher level of math. Also, a box plot can be drawn from a cumulative frequency curve.

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## Comments 1 comment

Heck--I understood this?!?! a miracle!! A box does set it up for me. I found I enjoyed this very much. You have this laid out beautifully and it is easy to understand. Keep up the great HUBS. I must give this an “Up ONE and awesome.” I'm always your fan! RJ

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