21M.1.SL.TZ1.4

pestleMathematicsAASLPaper 121M· sl-4-1-concepts-reliability-and-sampling-techniquessource ↗

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 $L$ and $U$ are the lower and upper quartiles respectively.

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

Find the minimum possible value of $U$ .

[3]

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

[2]

Markscheme / solution

attempt to use definition of outlier

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

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

minimum value of $U = 45$ A1

[3 marks]

attempt to use interquartile range (M1)

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

minimum value of $L = 25$ A1

[2 marks]

Examiners’ report

[N/A]