June 2024 Paper 2 Q11

OCR ACurrent spec8 marksData Processing

11 The chart below represents the percentage increases (PI) in the numbers of employees using four different methods of travel to work from 2001 and 2011, in five different Local Authorities (LAs) in Wales.

Shaded chart. Rows: Caerphilly, Merthyr Tydfil, Neath Port Talbot, Rhondda Cynon Taff, The Vale of Glamorgan. Columns (method of transport): Work mainly at or from home; Underground, metro, light rail, tram; Train; Driving a car or van. Each cell is shaded by a key of five PI bands: -10% to +10% (white), +10% to +30% (light grey), +30% to +50% (mid grey), +50% to +90% (dark grey), above +90% (black). Work from home: light, mid, light, light, mid. Underground etc: dark, black, white, black, dark. Train: dark, black, black, dark, dark. Driving: light, mid, light, light, light

(a)

(i) State, with a reason, which of the four methods of transport probably had the greatest overall percentage growth in these LAs between 2001 and 2011. [1]

(ii) Explain why your answer to part (a)(i) is not definite. [1]

(b) A student suggests that the chart can be used to estimate the total percentage change for these methods of transport in each individual LA.
Give two reasons why the student is likely to be wrong. [2]

(c) A student wants to investigate the trend from 2001 to 2011 in numbers using underground, metro, light rail or tram. The actual numbers of people using these methods in these LAs in 2001 were all less than 50 (and in one case was 4).
Explain why this means that the chart does not provide very helpful information for the student. [1]

(d) Let \(D\) denote the number of people in the Vale of Glamorgan whose usual method of travel to work is “Driving a car or van”, and let \(H\) denote the number of people in the Vale of Glamorgan who “Work mainly at or from home”.
Between 2001 and 2011 the increase in \(D\) was approximately 3.5 times the increase in \(H\).
Use this fact and the information in the chart to estimate the ratio \(D : H\) in 2001. [3]

Mark scheme (a)

Scheme	Marks	AO
(i) Train, because all increases over 50%	B1	2.2b
	[1]
(ii) The chart does not show where in the range each value is Or We do not know the (relative) sizes of each LA	B1	2.3
	[1]

Notes

(a)(i) B1: Must specify Train and give a reason. Any sensible reason related to chart, e.g.:

“Train has two of highest category and three of the 2^nd highest”
May refer to colours (e.g. dark, darker, darkest)

(a)(ii) B1: Any sensible reason relating to either ‘exact values’ or ‘actual/relative sizes of each LA’. Examples:

“we do not know exact values because the data is grouped” B1
“grouped” (without reference to exact values) B0
“increases could be much higher than 90%” B1
“low % of high number may be greater than high % of low number” B1
“not all workers accounted for” B0
“may be errors in data” B0

NB throughout this question, do not credit reasons that don’t relate to the question or that attempt to criticise the data set (rather than the chart/presentation and reasoning from it).

Mark scheme (b)

Scheme	Marks	AO
Do not know the initial proportions of each mode of transport	B1	2.3
Do not know the exact % increases	B1	2.4
	[2]

Notes

B1 B1: Any 2 distinct correct reasons. Examples:

“% ranges are wide” B1
“Do not know the upper limit for +90% PI” B1
“Do not know values within -10 to +10%” B1
“Do not know baseline values for each mode” B1
“size of the LAs” (not relevant here) B0

Do not credit criticism of underlying data or grouping of modes of transport (e.g. walking/working from home) B0

Mark scheme (c)

Scheme	Marks	AO
(Small) changes in these small numbers will lead to large % increases (which may give a misleading impression of the overall trend).	B1	2.4
	[1]

Notes

B1: Must refer to numbers or absolute values, not just %, e.g.:

“actual increases small (so hard to see trend)” B1
Do not credit references to grouped data / exact values here (not relevant) B0

Mark scheme (d)

Scheme	Marks	AO
Increase in \(D\) is 20% and in \(H\) is 40%	M1	3.1a
\(0.2D_{01} \approx 3.5 \times 0.4H_{01}\)	M1	1.1
\(D : H\) is \(7 : 1\)	A1	2.2b
	[3]

Notes

M1: M1 for sight of midpoints: 20% and 40%

Allow 0.2 and 0.4
Condone 1.2 and 1.4

Alternatively may see comparison of corresponding lower and upper bounds e.g. 10% -> 30% and 30% -> 50% (this leads to an estimate of 8.15) – M1

M1: For setting up two expressions and correctly using 3.5 (must be on the correct side). Do not accept 1.2, 1.4 here (NB \(3.5 \times 0.4 = 1.4\))
Allow = instead of \(\approx\)
Must be using two estimates for midpoints or considering both sets of lower/upper bounds

A1: Accept 3.5:0.5. If lower and upper bounds used, accept 8(.15):1
Need not be given as a ratio: accept \(\frac{D_{01}}{H_{01}} \approx 7\) oe but not \(D = 7H\)
Note that 7:2 often comes from not using any information from the chart (M0M0A0)