Box and whisker diagrams

A box and whisker diagram

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A box and whisker diagram

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25% of data 25% of data 25% of data 25% of data

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A set of test results in a box and whisker diagram

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The terminology!

5

upper quartile

medianlowerquartil

e

lower extrem

e

upper extrem

e

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).

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Quick ‘recap’ questions:

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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.

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A set of test results in a box and whisker diagram: some initial questions

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1. What is the range of the test data? Ans: 120 – 30 = 90

2. Give the median mark for the test. Ans: 603. What is the interquartile range of the marks?.

Ans: 85 - 40 = 45 (the range of the middle 50% of the class.)

Question on range of data:

A box and whisker plot appears below.

Work out the range of the data shown below:

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.)

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

Num

ber

of

abse

nce

s

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?

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

Num

ber

of

abse

nce

s

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?

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

Num

ber

of

abse

nce

s

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?

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

Num

ber

of

abse

nce

s

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?

http://www.bbc.co.uk/schools/gcsebitesize/maths/statistics/representingdata3hirev6.shtml

http://www.education.gov.uk/schools/careers/traininganddevelopment/professional/b00211213/numeracy/areas/box-and-whiskers

https://www.khanacademy.org/math/probability/descriptive-statistics/Box-and-whisker%20plots/v/reading-box-and-whisker-plots

http://www.youtube.com/watch?v=QXp596gfG3c

Need things explained again?

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/downloadableworksheets/tdamaths/bw&cumulative.pdf

Box and Whisker worksheet – Word document to download

Want to practise?

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You can suggest additional resources by adding a comment below our numeracy

blog post.

Good luck! 20