4MA0 Higher January 2017 Paper 3 Q11

EdexcelHigherOld spec6 marksCumulative Frequency

11 The frequency table gives information about the lengths of time 100 people spent in a coffee shop.

Time (\(t\) minutes)	Frequency
\(0 \lt t \leqslant 20\)	4
\(20 \lt t \leqslant 40\)	12
\(40 \lt t \leqslant 60\)	26
\(60 \lt t \leqslant 80\)	42
\(80 \lt t \leqslant 100\)	12
\(100 \lt t \leqslant 120\)	4

(a) Complete the cumulative frequency table. (1)

Time (\(t\) minutes)	Cumulative frequency
\(0 \lt t \leqslant 20\)
\(0 \lt t \leqslant 40\)
\(0 \lt t \leqslant 60\)
\(0 \lt t \leqslant 80\)
\(0 \lt t \leqslant 100\)
\(0 \lt t \leqslant 120\)

(b) On the grid, draw a cumulative frequency graph for your table. (2)

Cumulative frequency grid: cumulative frequency from 0 to 100 on the vertical axis, time in minutes from 0 to 120 on the horizontal axis

(d) Use your graph to find an estimate for the number of these people who spent longer than 70 minutes in the coffee shop. (2)

Scheme	Marks
4, 16, 42, 84, 96, 100 Answer: 4, 16, 42, 84, 96, 100	B1
	(1)

Mark scheme (b)

Scheme	Marks
(20, 4) (40, 16) (60, 42) (80, 84) (100, 96) (120, 100)	M1
correct cf graph	A1
	(2)

Notes

M1: (ft from sensible table i.e. clear attempt at addition)

for at least 4 points plotted correctly at end of interval
or
for all 6 points plotted consistently within each interval in the freq table at the correct height

A1: accept curve or line segments
accept curve that is not joined to (0,0)

Scheme	Marks
46 - 48	B1
	(1)

Mark scheme (d)

Scheme	Marks
E.g. reading from graph at \(t = 70\)	M1
36 – 38	A1
	(2)
	(6 marks)

Notes

M1: for evidence of using graph at \(t = 70\)

ft from a cumulative frequency graph provided method is shown

A1: 100 – ‘63’ ft from a cf graph

ft from a cumulative frequency graph provided method is shown