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Numeracy Intermediate June 2024 Unit 1 Q8

WJECIntermediateCurrent spec9 marksBox PlotsCumulative Frequency

8.

(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: cumulative frequency from 0 to 200 against time (s) from 0 to 60. Points (10, 0), (20, 20), (30, 80), (40, 170) and (50, 200) 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 on a time (s) axis from 0 to 60: minimum 8, lower quartile 20, median 36, upper quartile 46, maximum 50

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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