Box Plots: Eduqas GCSE Higher June 2022 Paper 2 Q16

Higher June 2022 Paper 2 Q16

EduqasHigherCurrent spec7 marksBox Plots Cumulative Frequency

16. As part of an experiment two groups of people, A and B, took the same general knowledge test.

The test had a maximum of 100 marks.

(a)

The first two columns of the table summarise the results of the test for the 45 people in Group A.

Mark	Frequency	Cumulative Frequency
\(0 \lt p \leqslant 20\)	0	0
\(20 \lt p \leqslant 40\)	3	3
\(40 \lt p \leqslant 60\)	20
\(60 \lt p \leqslant 80\)	15
\(80 \lt p \leqslant 100\)	7

(i) Complete the cumulative frequency column. [1]

(ii) Explain why 60 is a reasonable estimate of the median mark. [1]

(b)

This box plot shows the distribution of the marks of the people in Group B.

Grid with a Mark axis from 20 to 100, rows labelled Group A (empty) and Group B; the Group B box plot has minimum 39, lower quartile 52, median 58, upper quartile 72 and maximum 82

(i)

For the people in Group A:

Minimum mark	Range	Lower Quartile	Median	Upper Quartile
23	76	49	60	75

Draw the box plot for Group A on the grid above. [3]

(ii) Make two comments to compare the results of Group A and Group B.
One comment must include an appropriate average.
The other comment must include a measure of spread. [2]

Comment 1 ……………………

Comment 2 ……………………

Mark scheme (a)

Scheme

Marks

Comments

(a)(i)

Mark	f	cf
\(0 \lt p \leqslant 20\)	0	0
\(20 \lt p \leqslant 40\)	3	3
\(40 \lt p \leqslant 60\)	20	23
\(60 \lt p \leqslant 80\)	15	38
\(80 \lt p \leqslant 100\)	7	45

(a)(ii)
Valid explanation e.g.
‘23 terms include all marks as far as 60’

Allow valid explanations based on 22.5th term.
Allow e.g.
‘23 people less than or equal to 60 and 22 people above 60

Must say more than ‘60 is in the middle group.’
FT ‘their 45’ providing from one error in arithmetic only

Answer: Group A box plot with whiskers at 23 and 99, box from 49 to 75 and median 60, drawn above the Group B box plot — Mark scheme (b)

Scheme	Marks	Comments
(b)(i) Correct box plot Left whisker 23, LQ 49, median 60, UQ 75 and right whisker 99	B3	B2 for complete box plot with four correct values B1 for any three values correctly plotted in a box plot or for maximum of 99 seen but not drawn on box plot.
(b)(ii) Valid comment comparing medians e.g. ‘On average, Group A did better than Group B as the median was 60 whereas Group B’s median was 58’ or ‘The medians are similar so there is not much difference between the groups.’	E1	Must be a comparison not simply a comment about one group Allow e.g. ‘Group A had a higher median (so did better on average)’. ’The average of group A is two marks higher’ ‘Group A had a higher average of 60’ as clearly using the median as the average. Do not allow e.g. ‘Group A had a median of 60 and Group B had a median of 58.’ (no comparison) ‘The medians are similar’ without further explanation. ‘On average Group A were better’, (no reference to median or comparison of values).
Valid comment comparing IQRs or ranges e.g. ‘Group B’s results were less varied than Group A’s as the IQR was 20 which was less than Group A’s which was 26’ or ‘Group B’s results were more consistent than Group A’s as the range was 43 compared to Group A’s range of 76.’	E1	Must be a comparison not simply a comment about one group Allow e.g. ‘Group B’s marks were more consistent as the IQR is smaller’ Do not allow e.g. ‘Group A had a range of 76 and Group B had a range of 43.’ (no comparison) Do not allow if values contradict the statement e.g. ‘Group B has lower range, only 20 but A’s range is 26’ need IQR not range here.
	(7)