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Higher June 2023 Paper 1 Q17

EduqasHigherCurrent spec9 marksCumulative FrequencyHistograms

17.

(a) Gracie has collected data about the heights of 30 giant sunflowers.
The table shows her results.
Height, \(h\) (m)\(3 \lt h \leqslant 3{\cdot}5\)\(3{\cdot}5 \lt h \leqslant 4\)\(4 \lt h \leqslant 4{\cdot}5\)\(4{\cdot}5 \lt h \leqslant 5\)
Frequency58125
Gracie attempts to draw a cumulative frequency diagram.
Gracie’s cumulative frequency graph: points plotted at (0, 0), (3.25, 5), (3.75, 13), (4.25, 25) and (4.75, 30) joined with straight lines
Make two different criticisms of Gracie’s diagram. [2]
(b) Gracie also collects data about the amount of money each of a group of 40 gardeners spent on their gardens during the months of April and May.
The table shows the data for April.
Amount for April, (£\(x\))\(0 \lt x \leqslant 30\)\(30 \lt x \leqslant 40\)\(40 \lt x \leqslant 50\)\(50 \lt x \leqslant 60\)\(60 \lt x \leqslant 80\)
Frequency691258
(i) Draw a histogram to represent the data for April. [4]
Blank grid for a histogram: frequency density from 0 to 2 against amount for April, £x, from 0 to 90
(ii) The histogram below represents the data for May.
Histogram for May: frequency density 0.4 for 0 to 30, 1.5 for 30 to 40, 0.6 for 40 to 50 and 0.7 for 50 to 60
Calculate an estimate of how many more of the 40 gardeners spent £45 or less in May than spent £45 or less in April?
You must show all your working. [3]