Foundation June 2019 Paper 2 Q11

OCRFoundationCurrent spec6 marksScatter Diagrams & Correlation

11 A doctor records the ages, in years, and the heights, in centimetres, of 10 girls.

Age (years)	2	5	3	7	5	8	3	6	9	4
Height (cm)	85	115	93	120	110	125	90	117	127	103

The points for the first six girls are plotted on the scatter diagram.

(a) Plot the points for the remaining four girls. [2]

(b) Describe the type of correlation shown in the scatter diagram. [1]

(c) The doctor says that by using a line of best fit on the scatter diagram, the height of a 6-year-old girl is around 95 cm.

Does the scatter diagram support the doctor’s statement?
Explain your reasoning. [2]

(d) Explain why the scatter diagram and line of best fit should not be used to estimate the height of a 12-year-old girl. [1]

Answer	Marks	Part marks and guidance
Four points correctly plotted	2	B1 for 2 or 3 correct plots	Overlay gives guidance, tolerance ± ½ small square

Answer	Marks	Part marks and guidance
Positive	1		Ignore embellishments

Mark scheme (c)

Answer	Marks	Part marks and guidance
Ruled line of best fit	1		Use overlay for LOBF – ruled line should touch blue lines and should not go outside the yellow lines
No - it is too low oe	1		Eg No, at 95cm you’re only about age 3 SEE APPENDIX

Exemplar responses for the second mark of Q11c

Response	Mark
No, the LOF shows that the girl is 105cm (LOBF passing through (6, 105) but allow accuracy within 1 square vertically of line)	1
No because the LBF is further away	1
The scatter diagram doesn’t support the doctors statement, the diagram said that is around 117 cm the height	1
No, because the six year old on this diagram is 117 in height (this is ok without referring to LOBF as they are referring to the diagram)	1
No, the height would be around 114 (114 read from their LOBF or in range 110-120)	1
No, because the plotting is mostly at the top of the line, only (age) 3 at 95 (this last part is the alternative correct reason)	1
Because 6 is 117 on the diagram (No decision is stated)	0
Yes because in the SD there is a 6 yr old girl that has a height of 117 (Statement acceptable but wrong decision of yes)	0
No the height of a 9 year old is 110 (LOBF passes through (6, 115)	0
6 year olds are about 100 – 110 (giving a range 110 – 120 in the statement would earn the mark)	0 (1)

Mark scheme (d)

Answer	Marks	Part marks and guidance
Only have data on heights up to age 9 oe	1		e.g. the trend may not continue SEE APPENDIX

Exemplar responses for Q11d

Response	Mark
Because the graph has only been plotted from 2 – 9 years old so you would not get an accurate estimation.	1
Because the correlation of height with the age is not always the same	1
Because there has been no 12 year olds that were in the group of girls which means it may be an unfair assumption	1
Because the graph doesn't cover that age group and the growth process can change then	1
There is no data beyond a 9 year old so it would be unreliable	1
Because there are no points plotted for a 12 year old	1
You are missing 2 age groups not including 12 anyway so it wouldn’t be accurate	1
Because there is no original data on the diagram for anyone over 10	1
After 9 years points may not be near the line of best fit (Reference to trend in the given data changing is ok)	1
A 12 year old girl would be too tall for this diagram (reference to scale/size of axes rather than available data)	0
Because the line of best fit won't go that far because the graph only goes up to 135cm	0
Because it will go out of the graph	0
Because the line of best fit would say the 12 year old girl would be about 160cm	0
Because there is no height recorded (not enough)	0
Growth slows down as they get taller (Referring to trend in growth scores 0)	0
This is because at this age girls will be different heights because of puberty	0