Box Plots

Instructions Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help. When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

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Isabella, Wednesday, April 26, 2017 "The formula for finding the median is a on N items is (N+1)/2. Why is there a 'plus one' in that formula? [Transum: Good question Isabella. The answer is here.]" Madison Davis, ABSS Schools Tuesday, April 21, 2020 "Is there a way to share the box plot level 1 activity without the answer key showing up at the bottom? [Transum: Whoops, that's a glitch. I have corrected it now. Thanks for the information]" Rmacy, Rmacy Sunday, August 20, 2023 "In Question 10, the max should be the maximum number of minutes. However, when we calculate the quartiles, should they be from the cumulative frequency or the number of minutes? And if so, do we the highest frequency (54) or the highest frequency on the graph which is 60? Would appreciate your guidance! [Transum: Yes the highest frequency is 54 despite the fact that the vertical axis goes all the way to 60. Use the graph to find the quartiles. Good luck.]" Transum, Wednesday, October 25, 2023 "The International Baccalaureate Mathematics AA Syllabus states "Awareness that different methods for finding quartiles exist and therefore the values obtained using technology and by hand may differ."." Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.

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Example

For discrete distributions, there is no universal agreement on selecting the quartile values, but for the purpose of this exercise, we'll use the most popular method:

The median is the value in the middle of the data set when it is arranged in order of size.
Use the median to divide the ordered data set into two halves. The median becomes the second quartile.
If there are an odd number of data points in the original ordered data set, do not include the median (the central value in the ordered list) in either half.
If there are an even number of data points in the original ordered data set, split this data set exactly in half.
The lower quartile value is the median of the lower half of the data. The upper quartile value is the median of the upper half of the data.

Read more about the methods for finding quartiles of discrete data in the December 2024 Transum Newsletter.

The interquartile range is the difference between the upper and lower quartiles:

IQR = Q_3 - Q_1.

Fact worth knowing: If a value is more that 1.5 × IQR above the upper quartile or below the lower quartile it is considered to be an outlier.

If you are using a TI-Nspire CX calculator did you know that it can draw a box plot for you? See GDC Essentials.

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.


1. This box plot shows the number of minutes patients spent in a dentist's waiting room. What is the median time in minutes?	minutes

2. This box plot shows the number of minutes passengers spent in an airport departure lounge. What is the minimum number of minutes spent waiting in the lounge?	minutes

3. This box plot shows the time (in minutes) spent commuting to work by a group of office workers. What is the maximum commute time in minutes?	minutes

4. This box plot shows the number of marks earned by the boys in a class test. What was the lower quartile?	marks

5. This box plot shows the number of marks earned by the girls in a class test. What was the upper quartile?	marks

6. This box plot shows the number of minutes passengers spent in a station waiting room. What is the range of times spent in the waiting room?	minutes

7. This box plot shows the number of minutes passengers spent in a different station waiting room. What is the inter-quartile range of times spent in the waiting room?	minutes

8. This box plot shows the lengths of leaves (in centimetres) collected by a botanist. Express the minimum length as a percentage of the maximum length.	%

9. This box plot shows the length (in inches) of fish recorded in a very large database. What percentage of the fish were longer than 60 inches?	%

10. This box plot shows the length (in milimetres) of worms recorded in a very large database. What percentage of the worms were less than 91mm long?	%

Box Plots

An exercise on reading and drawing box-and-whisker diagrams which represent statistical data.

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