16 The table shows information about the lengths of time that 120 people spent in a supermarket.
Time (\(t\) minutes)
Frequency
\(0 \lt t \leqslant 10\)
8
\(10 \lt t \leqslant 20\)
17
\(20 \lt t \leqslant 30\)
25
\(30 \lt t \leqslant 40\)
40
\(40 \lt t \leqslant 50\)
22
\(50 \lt t \leqslant 60\)
8
(a) Complete the cumulative frequency table.
Time (\(t\) minutes)
Cumulative frequency
\(0 \lt t \leqslant 10\)
\(0 \lt t \leqslant 20\)
\(0 \lt t \leqslant 30\)
\(0 \lt t \leqslant 40\)
\(0 \lt t \leqslant 50\)
\(0 \lt t \leqslant 60\)
(1)
(b) On the grid, draw a cumulative frequency graph for your table.(2)
(c) Use your graph to find an estimate for the median length of time spent in the supermarket by these people. (2)
Mark scheme (a)
Scheme
Marks
8, 25, 50, 90, 112, 120
B1
(1)
Notes
B1: cao
Mark scheme (b)
Scheme
Marks
Plotting points from table at ends of interval
B1
Points joined with curve or line segments
B1
(2)
Notes
B1: ± ½ sq ft from sensible table ie clear attempt to add frequencies
B1: ft from points if 4 or 5 correct or if all points are plotted consistently within each interval at the correct heights Accept cf graph which is not joined to the origin NB A bar chart, unless it has a curve going consistently through a point in each bar, scores no points.
Mark scheme (c)
Scheme
Marks
60 (or 60.5) indicated on cf graph or stated
M1
approx 33
A1
(2)
(5 marks)
Notes
M1: for 60 (or 60.5) indicated on cf axis or stated
A1: If M1 scored, ft from cf graph If no indication of method, ft only from correct curve & if answer is correct (± ½ sq tolerance) award M1 A1
