Higher June 2021 Paper 2 Q12

EdexcelHigherCurrent spec7 marksAverages (including IQR)Cumulative Frequency

12 The cumulative frequency table gives information about the distance, in kilometres, that each of 80 workers travel from home to work at Office \(A\).

Distance travelled (d km)	Cumulative frequency
\(0 \lt d \leqslant 5\)	17
\(0 \lt d \leqslant 10\)	32
\(0 \lt d \leqslant 15\)	57
\(0 \lt d \leqslant 20\)	70
\(0 \lt d \leqslant 25\)	76
\(0 \lt d \leqslant 30\)	80

(a) On the grid below, draw a cumulative frequency graph for the information in the table. (2)

Grid with Distance travelled (km) from 0 to 30 on the horizontal axis and Cumulative frequency from 0 to 80 on the vertical axis

(b) Use your graph to find an estimate for the median distance travelled. (1)

For Office \(B\), the median distance workers travel from home to work is 15 km and the interquartile range is 5 km.

(d) Use the information above to compare the distances that workers at Office \(A\) and workers at Office \(B\) travel from home to work.
Write down two comparisons. (2)

Mark scheme (a)

Scheme	Marks
	M1
(NB: a ‘bar chart’ type graph scores zero marks) Answer: correct cf graph	A1
	(2)

Notes

M1: 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 2.5, 7.5, 12.5, 17.5, 22.5, 27.5 or 0, 5, 10, 15, 20, 25) at the correct height

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

Mark scheme (b)

Scheme	Marks
If answer is in the given range, then award the mark – unless from obvious incorrect working Answer: 10.5 to 12	B1ft
	(1)

Notes

B1ft: accept answer in range 10.5 – 12 or ft their cumulative frequency graph (must be an ascending graph) (allow 1 small square tolerance)

Mark scheme (c)

Scheme	Marks
NB: readings are 5.5 – 7 and 15.5 – 17 (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 Distance axis at the correct points (or they can just show the correct readings))	M1ft
If answer is in the given range, then award the marks – unless from obvious incorrect working Answer: 8.5 to 11.5	A1ft
	(2)

Notes

M1ft: For correct use of LQ and UQ, 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 Distance axis (even if wrongly read scale) or clear marks on the graph and Distance axis that correspond to the correct readings or correct values from the Distance axis

A1ft: Accept a single value in range 8.5 to 11.5 or ft from their cumulative frequency graph provided method is shown

Mark scheme (d)

Scheme	Marks
not in context: office \(B\) workers have a higher median than office \(A\) workers oe in context: office \(B\) workers [tend to] travel further oe	B1
not in context: the IQR for office \(A\) workers is bigger than the IQR for office \(B\) workers oe in context: The distances for the office \(A\) workers are more spread out/more varied oe	B1
	(2)
	(7 marks)

Notes

B1: ft comparison of medians e.g. Office \(B\) workers travel further [but if they have a wrong median then correct comparison of this with the 15 km]
(Must compare to median in (b))

B1: ft comparison of IQR eg Office \(A\) distances are more spread (must compare to IQR in (c))
NB: To award both marks at least one comparison must be in context