22 Here is some information about the miles per gallon of 60 cars.
Miles per gallon, \(x\)
Frequency
\(40 \lt x \leqslant 50\)
6
\(50 \lt x \leqslant 60\)
16
\(60 \lt x \leqslant 70\)
28
\(70 \lt x \leqslant 80\)
10
(a) Draw a cumulative frequency graph. [3 marks]
(b) Use the graph to work out the interquartile range. [2 marks]
Mark scheme (a)
Answer
Mark
Comments
(6) 22 50 60
B1
cumulative frequency values may be implied by points plotted (\(\pm\) 0.5 square)
Points plotted with upper class boundaries and cf values (\(\pm\) 0.5 square)
B1ft
ft their cumulative frequencies must be increasing
Smooth curve or polygon (\(\pm\) 0.5 square)
B1ft
ft their cumulative frequencies must be increasing and not a single straight line
Additional guidance
Graphs may start from their first plotted point or from (40, 0) If the points are plotted at mid-points, with a point at (45, 6), the graph may start at (35, 0) (\(\pm\) 0.5 square) If the points are plotted at the lower bounds, with a point at (40, 6), the graph may start at (0, 0)
Graph starting at (0, 0), but otherwise correct
B1B1B0
Graph plotted at mid-points or lower class boundaries, but otherwise correct
B1B0B1
Graph ascends or descends after \(x = 80\)
B0 for 3rd mark
Bars drawn as well as correct graph
B1B1B0
Bars drawn without correct graph
max B1
Mark scheme (b)
Answer
Mark
Comments
One correct mpg reading for their graph from cf of 15(.25) or 45(.75) or horizontal lines from 15(.25) and 45(.75) only to their graph or 15(.25) and 45(.75) indicated as the cf values for the quartiles
