19N.1.SL.TZ0.T_15

pestleMathematicsAISLPaper 119N· sl-4-2-histograms-cf-graphs-box-plotssource ↗

Stephen was invited to perform a piano recital. In preparation for the event, Stephen recorded the amount of time, in minutes, that he rehearsed each day for the piano recital.

Stephen rehearsed for $32$ days and data for all these days is displayed in the following box-and-whisker diagram.

Stephen states that he rehearsed on each of the $32$ days.

Write down the median rehearsal time.

[1]

State whether Stephen is correct. Give a reason for your answer.

[2]

On $k$ days, Stephen practiced exactly $24$ minutes.

Find the possible values of $k$ .

[3]

Markscheme / solution

$42$ (minutes) (A1) (C1)

[1 mark]

Stephen is correct. (A1)

the minimum rehearsal time is greater than zero (R1)

he rehearsed at least $20$ minutes every day (R1) (C2)

Note: Do not award (A1)(R0). Accept equivalent reasoning based on the box-and-whisker diagram.

[2 marks]

$0, 2, 3, 4, \dots, 15$ (A1)(A1)(A1) (C3)

Note: Award (A1)(A1) for each correct endpoint of the interval, (A1) for indication of integer values, except 1, between their endpoints.

[3 marks]

Examiners’ report

[N/A]