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Numeracy Higher June 2024 Unit 1 Q4

WJECHigherCurrent spec9 marksBox PlotsCumulative Frequency

4.

(a) On 1st June last year, 200 customers used cash to pay at Shop Lil.
The cumulative frequency diagram represents the time each of these 200 customers waited to be given change at the checkout.
Cumulative frequency graph on a grid, Time (s) from 0 to 60 and cumulative frequency from 0 to 200, with plotted points joined by straight lines
(i) How many of these customers waited between 30 and 50 seconds for their change? [2]
(ii) Use the graph to estimate the median time these 200 customers waited for their change.
Circle your answer. [1]

24 seconds    32 seconds    38 seconds    80 seconds    100 seconds

(iii) Calculate the fraction of these 200 customers who waited 40 seconds or longer for their change.
Give your answer in its simplest form. [2]
(b) On 1st June this year, the manager at Shop Lil drew a box-and-whisker plot of the times 200 customers waited for their change at the checkout.
Box-and-whisker plot drawn on a grid with a Time (s) axis from 0 to 60

Based on the results of these 200 customers, the manager made the following statements. Complete the statements.

(i) “On 1st June this year, 50% of our customers were given their change in …………… seconds or less.” [1]
(ii) “On 1st June this year, the interquartile range of the times taken to give customers their change was …………… seconds.” [2]
(c) Consider the 50 customers waiting the longest times to get their change on 1st June last year and this year.
Has the speed of giving change at the checkout improved since last year?

Yes ☐    No ☐

You must give a reason for your answer. [1]

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