June 2023 Paper 2 Q14

OCR MEICurrent spec8 marksCorrelation & Regression Large Data Set

14 The pre-release material contains information concerning the median income of taxpayers in £ and the percentage of all pupils at the end of KS4 achieving 5 or more GCSEs at grade A*–C, including English and Maths, for different areas of London.

Some of the data for 2014/15 is shown in Fig. 14.1.

Fig. 14.1

	Median Income of Taxpayers in £	Percentage of Pupils Achieving 5 or more A*–C, including English and Maths
City of London	61 100	#N/A
Barking and Dagenham	21 800	54.0
Barnet	27 100	70.1
Bexley	24 400	55.0
Brent	22 700	60.0
Bromley	28 100	68.0

A student investigated whether there is any relationship between median income of taxpayers and percentage of pupils achieving 5 or more GCSEs at grade A*–C, including English and Maths.

(a) With reference to Fig. 14.1, explain how the data should be cleaned before any analysis can take place. [1]

After the data was cleaned, the student used software to draw the scatter diagram shown in Fig. 14.2.

Fig. 14.2: scatter diagram of percentage of students (40 to 75) against median income in pounds (15 000 to 40 000); most points cluster between 20 000 and 30 000 with percentages 52 to 73, and a few points between 31 000 and 39 000 — Fig. 14.2

The student calculated that the product moment correlation coefficient for these data is 0.3743.

(b) Give two reasons why it may not be appropriate to use a linear model for the relationship between median income of taxpayers in £ and the percentage of all pupils at the end of KS4 achieving 5 or more GCSEs at grade A*–C. [2]

The student carried out some further analysis. The results are shown in Fig. 14.3.

Fig. 14.3

	median income of taxpayers in £	percentage of pupils achieving 5+ A*–C
mean	27 216	61.0
standard deviation	4177.5	5.32

The student identified three outliers in total.

(c)

Use the information in Fig. 14.3 to determine the range of values of the median income of taxpayers in £ which are outliers.
Use the information in Fig. 14.3 to determine the range of values of the percentage of all pupils at the end of KS4 achieving 5 or more GCSEs at grade A*–C which are outliers.
On the copy of Fig. 14.2 in the Printed Answer Booklet, circle the three outliers identified by the student.

[4]

The student decided to remove these outliers and recalculate the product moment correlation coefficient.

(d) Explain whether the new value of the product moment correlation coefficient would be between 0.3743 and 1 or between 0 and 0.3743. [1]

Mark scheme (a)

Scheme	Marks	AO
discard City of London (as part of the data not available) or discard any regions where one or more pieces of data are missing oe	B1	2.4
	[1]

Notes

B1: LDS advantage
do not allow if answer spoiled
eg because it’s an anomaly,
eg because it’s an outlier,

Mark scheme (b)

Scheme	Marks	AO
scatter does not look linear oe	B1	3.4
pmcc not close to 1 oe	B1	3.4
	[2]

Notes

B1: ignore extra comments unless they contradict an otherwise correct answer

The scatter diagram with three points circled: the highest point (about 29 000, 73) and the two points at about (35 800, 64.6) and (38 600, 67.2) — Mark scheme (c)

Scheme	Marks	AO
\(27216 \pm 2 \times 4177.5\) or \(61.0 \pm 2 \times 5.32\)	M1	1.1
\(m < 18861\) or \(m > 35\,571\)	A1	1.1
percentage \(< 50.36\) or percentage \(> 71.64\)	A1	1.1
	A1	1.1
	[4]

Mark scheme (d)

Scheme	Marks	AO
between 0 and 0.3743 since eg outliers gave a false impression of linearity eg scatter will be more like a circle	B1	2.4
	[1]

Notes

B1: need to refer to the shape of the scatter oe