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Date	May 2021	Marks available	2	Reference code	21M.1.SL.TZ1.4
Level	Standard Level	Paper	Paper 1 (without calculator)	Time zone	Time zone 1
Command term	Hence and Find	Question number	4	Adapted from	N/A

Question

A research student weighed lizard eggs in grams and recorded the results. The following box and whisker diagram shows a summary of the results where $L$ $L$ and $U$ $U$ are the lower and upper quartiles respectively.

The interquartile range is $20$ $20$ grams and there are no outliers in the results.

Find the minimum possible value of $U$ $U$ .

[3]

a.

Hence, find the minimum possible value of $L$ $L$ .

[2]

b.

Markscheme

attempt to use definition of outlier

$1.5 \times 20 + Q_{3}$ $1.5 \times 20 + Q_{3}$ (M1)

$1.5 \times 20 + U \geq 75$ $1.5 \times 20 + U \geq 75$ ( $\Rightarrow U \geq 45$ $\Rightarrow U \geq 45$ , accept $U > 45$ $U > 45$ ) OR $1.5 \times 20 + Q_{3} = 75$ $1.5 \times 20 + Q_{3} = 75$ A1

minimum value of $U = 45$ $U = 45$ A1

[3 marks]

a.

attempt to use interquartile range (M1)

$U - L = 20$ $U - L = 20$ (may be seen in part (a)) OR $L \geq 25$ $L \geq 25$ (accept $L > 25$ $L > 25$ )

minimum value of $L = 25$ $L = 25$ A1

[2 marks]

b.

Examiners report

[N/A]

a.

[N/A]

b.

Syllabus sections

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

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