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Date May Example question Marks available 2 Reference code EXM.1.SL.TZ0.5
Level Standard Level Paper Paper 1 Time zone Time zone 0
Command term Find Question number 5 Adapted from N/A

Question

A set of data comprises of five numbers  x 1 , x 2 , x 3 , x 4 , x 5  which have been placed in ascending order. 

Recalling definitions, such as the Lower Quartile is the  n + 1 4 t h  piece of data with the data placed in order, find an expression for the Interquartile Range.

[2]
a.

Hence, show that a data set with only 5 numbers in it cannot have any outliers.

[5]
b.

Give an example of a set of data with 7 numbers in it that does have an outlier, justify this fact by stating the Interquartile Range.

[2]
c.

Markscheme

L Q = x 1 + x 2 2 , U Q = x 4 + x 5 2 , I Q R = x 4 + x 5 x 1 x 2 2        M1A1

[2 marks]

a.

U Q + 1.5 I Q R = 1.25 x 4 + 1.25 x 5 0.75 x 1 0.75 x 2 x 5       M1A1

Since  1.25 x 4 + 0.25 x 5 0.75 x 1 + 0.75 x 2  due to the ascending order.      R1

Similarly  L Q 1.5 I Q R = 1.25 x 1 + 1.25 x 2 0.75 x 4 0.75 x 5 x 1       M1A1

Since  0.25 x 1 + 1.25 x 2 0.75 x 3 + 0.75 x 4  due to the ascending order.

So there are no outliers for a data set of 5 numbers.      AG

[5 marks]

b.

For example 1, 2, 3, 4, 5, 6, 100 where  I Q R = 4      A1A1

[2 marks]

c.

Examiners report

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b.
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c.

Syllabus sections

Topic 4—Statistics and probability » SL 4.1—Concepts, reliability and sampling techniques
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Topic 4—Statistics and probability

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