Box Plots and Interquartile Range

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Box Plots and Interquartile Range — Free MYP3 Mathematics Practice Questions

1QuestionCalculating and Interpreting the Interquartile RangeConcept Practice

2 marks~3 minCriterion A

The box plot below shows the distribution of test scores for a class.

Minimum: 40 —

Q_1

: 55 — Median: 70 —

Q_3

: 85 — Maximum: 100

Calculate the interquartile range (IQR) of the test scores. [2]

IQR = Q_3 - Q_1

Solutions

2QuestionComparing Data Sets Using Box PlotsAssessment Practice

5 marks~8 minCriterion C

The box plots below show the mathematics exam scores for Class A and Class B.

Class A	Minimum 45	$Q_1 = 55$	Median $= 65$	$Q_3 = 75$	Maximum 90
Class B	Minimum 50	$Q_1 = 60$	Median $= 70$	$Q_3 = 80$	Maximum 95

Calculate the interquartile range (IQR) for each class. [2]

Compare the medians of the two classes. Explain what this tells you about overall performance. [1]

A student claims: "Class B performed better overall and had more consistent scores." Using your results from (a) and (b), analyse whether this claim is fully correct, partially correct, or incorrect. Justify your answer. [2]

Solutions

3QuestionComparing Data Sets Using Box PlotsAssessment Practice

6 marks~9 minCriterion D

Two mathematics classes took the same test. Their results are shown in the box plots.

Class A	median $= 72$	$\text{IQR} = 18$	range $= 45$
Class B	median $= 68$	$\text{IQR} = 10$	range $= 25$

State the median score for each class. [1]

Compare the IQRs of the two classes. Explain what the difference in IQRs indicates about the consistency of scores in each class. [2]

The principal wants to award a prize to the class that performed better overall. Analyse whether the median alone is sufficient to make this decision, using the IQR and range to support your answer. [3]

Solutions

4QuestionDrawing Box Plots from Data SetsAssessment Practice

6 marks~9 minCriterion B

Five data sets, each with a median of 10, are shown below.

Data Set A:

2, 6, 10, 14, 18

(range

= 16

)
Data Set B:

4, 7, 10, 13, 16

(range

= 12

)
Data Set C:

6, 8, 10, 12, 14

(range

= 8

)
Data Set D:

8, 9, 10, 11, 12

(range

= 4

)
Data Set E:

0, 5, 10, 15, 20

(range

= 20

)

Calculate the IQR for each data set. Show your working. [2]

Describe the relationship between the range and the IQR for these data sets, and state a general rule linking IQR to range for symmetric, equally spaced sets of five values. [2]

A new data set has the same structure, a median of 10, and a range of 24. Calculate the IQR you would expect, then verify your answer by finding

Q_1

and

Q_3

for the data set

-2, 4, 10, 16, 22

. [2]

Solutions

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