Support material on box and whisker diagrams produced as part of a pilot project to assist higher education tutors who are faced with demands, across all 4 nations of the UK, to improve the numeracy skills of all those studying in order to work with children and young people.

1. Box and whisker diagrams

2. A box and whisker diagram
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Click on the loudspeaker symbol in the title box of
this slide to hear the commentary.
.

3. A box and whisker diagram
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Click on the loudspeaker symbol in the title box of
this slide to hear the commentary.
25% of data 25% of data 25% of data 25% of data

4. 30 120
A set of test results in a box and
whisker diagram
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856040
Click on the loudspeaker symbol in the title box of this
slide to hear the commentary.

5. The terminology!
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upper
quartile
medianlower
quartile
lower
extreme
upper
extreme
The five points on a box and whisker plot gives you the upper & lower
extreme values (numbers) of the data (the range or spread of the
data), the upper & lower quartiles (the interquartile range or spread of
the middle 50% of the data) and the median (centre point of the data).
(Click on the loudspeaker symbol in the title box of this slide if you want to hear
the commentary. Then listen to the recap on the next slide).

6. 30 120
Quick ‘recap’ questions:
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856040
1. What is the range of the test data?
2. Give the median mark for the test.
3. What is the interquartile range of the marks?
Answers on next slide.

7. 30 120
A set of test results in a box and whisker
diagram: some initial questions
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856040
1. What is the range of the test data? Ans: 120 – 30 = 90
2. Give the median mark for the test. Ans: 60
3. What is the interquartile range of the marks?.
Ans: 85 - 40 = 45 (the range of the middle 50%
of the class.)

8. Question on range of data:
A box and whisker plot appears below.
Work out the range of the data shown below:

9. Answer:
A box and whisker plot appears below.
The range of the data is:
Answer: 83
(Not 17-100 although that is a common mistake.
The range is a single number so taking the highest value, subtract
the lowest value. In this case 100 – 17 = 83.)

10. A box & whisker question: median
The box & whisker chart opposite
shows absence data for five year
groups in term one.
Which year group had the smallest
median number of absences?
Absence data for term 1
Numberofabsences

11. Answer:
The box & whisker chart opposite
shows absence data for five year
groups in term 1.
Which year group had the smallest
median number of absences?

12. A box & whisker question on range:
The box & whisker chart opposite
shows attendance data for five
year groups in term one.
Which year group had the smallest
interquartile range of absences?
Absence data for term 1
Numberofabsences

13. Answer:
The box & whisker chart opposite
shows attendance data for five
year groups in term one.
Which year group had the smallest
interquartile range of absences?

14. Another box & whisker question:
The box & whisker chart opposite
shows attendance data for five
year groups in term one.
Which year group had half of its
members recording 6 or more
absences?
Absence data for term 1
Numberofabsences

15. Answer:
The box & whisker chart opposite
shows attendance data for five
year groups in term one.
Which year group had half of its
members recording 6 or more
absences?

16. Another box & whisker question:
The box & whisker chart opposite
shows attendance data for five
year groups in term one.
Which year group had over three
quarters of its members recording
6 or more absences?
Absence data for term 1
Numberofabsences

17. Answer:
The box & whisker chart opposite
shows attendance data for five
year groups in term one.
Which year group had over three
quarters of its members recording
6 or more absences?

18. http://www.bbc.co.uk/schools/gcsebitesize/maths/statistics/representingdata3hire
http://www.education.gov.uk/schools/careers/traininganddevelopment/profession
https://www.khanacademy.org/math/probability/descriptive-statistics/Box-and-wh
http://www.youtube.com/watch?v=QXp596gfG3c
Need things explained again?

19. http://www.brainingcamp.com/resources/math/box-plots/questions.php
http://www.jmap.org/JMAP/RegentsExamsandQuestions/PDF/WorksheetsByPI-
Topic/IntegratedAlgebra/Statistics_and_Probability/A.S.6.BoxandWhiskerPlots1.
pdf
http://studentzone.roehampton.ac.uk/howtostudy/onlinemathsmaterials/downloa
dableworksheets/tdamaths/bw&cumulative.pdf
Box and Whisker worksheet – Word document to download
Want to practise?
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20. You can suggest additional resources by adding a
comment below our numeracy blog post.
Good luck!
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