4MA0 Higher June 2014 Paper 3 Q11

EdexcelHigherOld spec8 marksCumulative Frequency Grouped Data

11 The table gives information about the speed, in km/h, of 180 vehicles passing a speed checkpoint.

Speed (\(v\) km/h)	Frequency
\(40 \lt v \leqslant 50\)	4
\(50 \lt v \leqslant 60\)	52
\(60 \lt v \leqslant 70\)	60
\(70 \lt v \leqslant 80\)	34
\(80 \lt v \leqslant 90\)	18
\(90 \lt v \leqslant 100\)	12

(a) Write down the modal class. (1)

(b) Work out an estimate for the probability that the next vehicle passing the speed checkpoint will have a speed of 60 km/h or less. (2)

Speed (\(v\) km/h)	Cumulative frequency
\(40 \lt v \leqslant 50\)
\(40 \lt v \leqslant 60\)
\(40 \lt v \leqslant 70\)
\(40 \lt v \leqslant 80\)
\(40 \lt v \leqslant 90\)
\(40 \lt v \leqslant 100\)

(1)

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

Blank grid: cumulative frequency from 0 to 200 against speed (v km/h) from 40 to 100

(2)

(e) The police decide to fine the driver of any vehicle passing the speed checkpoint at a speed of more than 84 km/h.
Use your graph to find an estimate for the number of drivers the police decide to fine.
Show your method clearly. (2)

Scheme	Marks
\(60 \lt v \leqslant 70\)	B1
	(1)

Mark scheme (b)

Scheme	Marks
	M1
\(\dfrac{56}{180}\) oe	A1
	(2)

Notes

M1: for \(\dfrac{56}{a}\) with \(a > 56\) or \(\dfrac{b}{180}\) with \(b < 180\) or 0.31 or 31%

or \(\dfrac{4 + 52}{4 + 52 + 60 + 34 + 18 + 12}\)

A1: Accept answer written as an equivalent fraction, (eg \(\frac{14}{45}\)), or 0.311... (accept if first 3 SF correct) or 31.1...% (accept if first 3 SF correct)
M1A0 for 56 : 180 or 14 : 45 oe

Scheme	Marks
4, 56, 116, 150, 168, 180	B1
	(1)

Mark scheme (d)

Scheme	Marks
All 6 plotted correctly Answer: points plotted	B1
Curve or line segments	B1
	(2)

Notes

B1: All 6 points plotted correctly \(\pm\frac{1}{2}\) sq

B1: ft curve/line segments from points if 4 or 5 plotted correctly or if all 6 points are plotted consistently within each interval of the frequency table at the correct heights (\(\pm\frac{1}{2}\) sq).
Accept curve which is not joined to (40 , 0)

Mark scheme (e)

Scheme	Marks
vertical line or mark drawn at 84 km/or horizontal line corresponding to speed = 84km (± ½ sq) on cf graph.	M1
20 – 26 inclusive	A1
	(2)
	(8 marks)

Notes

M1: for 84 indicated on cf graph

A1: If M1 scored from 84 indicated on graph, ft from cf graph.
If M1 not scored from 84 indicated on graph, ft only from a correct curve / line segments. If their answer comes from their curve (± ½ sq) then award M1A1.