Higher January 2023 Paper 1R Q11

EdexcelHigherCurrent spec6 marksCumulative Frequency

11 The table shows information about the times, in minutes, that 80 patients had to wait to see a doctor.

Time (\(W\) minutes)	Frequency
\(0 \lt W \leqslant 10\)	7
\(10 \lt W \leqslant 20\)	10
\(20 \lt W \leqslant 30\)	15
\(30 \lt W \leqslant 40\)	32
\(40 \lt W \leqslant 50\)	16

(a) Complete the cumulative frequency table below.

Time (\(W\) minutes)	Cumulative frequency
\(0 \lt W \leqslant 10\)
\(0 \lt W \leqslant 20\)
\(0 \lt W \leqslant 30\)
\(0 \lt W \leqslant 40\)
\(0 \lt W \leqslant 50\)

(1)

(b) On the grid below, draw a cumulative frequency graph for your table.

Blank grid: time in minutes from 0 to 50 on the horizontal axis and cumulative frequency from 0 to 80 on the vertical axis

(2)

(d) Use your graph to find an estimate for the interquartile range. (2)

Scheme	Marks
7, 17, 32, 64, 80	B1
	(1)

Mark scheme (b)

Scheme	Marks
	M1ft
(NB: a ‘bar chart’ type graph scores zero marks) Answer: correct cf graph	A1
	(2)

Notes

M1ft: for at least 4 points plotted correctly at end of interval or for all points plotted consistently within each interval of the associated frequency table (eg at 5, 15, 25, 35, 45 or 0, 10, 20, 30, 40) at the correct height.
ft their table dep on one error only in the table

A1: All points plotted correctly at end of interval (tolerance 1 small square – there is an overlay) and joined with a curve or line segments; accept curve that is not joined at (0, 0).

Scheme	Marks
Accept a single value in the range OR ft their cf graph Answer: 33	B1ft
	(1)

Mark scheme (d)

Scheme	Marks
NB: readings are 21 - 23 and 37 - 39 (but for this M1 these do not have to be correct if correct working is shown – eg lines or marks indicating use of CF 20 (or 20.25) and CF 60 (or 60.75) with an indication on the Time axis at the correct points (or they can just show the correct readings))	M1ft
Accept a single value in the range OR ft their cf graph Answer: 16	A1ft
	(2)
	(6 marks)

Notes

M1ft: For correct use of LQ and UQ and subtraction, ft from a cum freq graph provided method is shown – eg a line horizontally to the graph from readings of CF 20 and CF 60 to meet the graph and then a vertical line to the Time axis (even if wrongly read scale) or clear marks on the graph and Time axis that correspond to the correct readings or correct values from the Time axis

A1ft: Accept a single value in range 15 to 17 or ft from their cumulative frequency graph provided method is shown eg subtraction of values that would be correct for their graph