Box Plots: WJEC GCSE Numeracy Higher November 2022 Unit 1 Q3

Numeracy Higher November 2022 Unit 1 Q3

WJECHigherCurrent spec8 marksBox Plots Cumulative Frequency

(a) The lengths of the 60 yachts in Eog Marina were measured.
The results are shown in the cumulative frequency diagram below.

The shortest yacht has a length of 3 m.
The longest yacht has a length of 22 m.

Use the information above to complete a box-and-whisker diagram on the graph paper below. [3]

(b) The lengths of the 68 yachts in Clwyd Marina were measured.

For these yachts:

(i) Calculate how many of the yachts in Clwyd Marina have lengths greater than 10 m. [2]

…………… yachts

(ii) In which marina, Eog or Clwyd, is the interquartile range of the lengths of the yachts greater?

Eog Marina ☐ Clwyd Marina ☐

You must show all your working. [2]

(iii) In which marina is the longest yacht?

Eog Marina ☐ Clwyd Marina ☐ Can’t tell ☐

You must give a reason for your answer. [1]

Mark scheme (a)

Scheme	Marks	Comments
Whiskers at 3 m and 22 m	B1	Ignore if lines omitted from the ends of the whiskers Must be the least and greatest values shown
Unambiguous values or box with LQ 5 m and UQ 20 m	B1	May be seen in working, must be clearly LQ and UQ Check cumulative frequency diagram If not clearly labelled in working or on the graph, they must be no other values given between the least and the LQ, and the greatest and the UQ
Median at 15 m	B1	May be seen in working, must be clearly the median Check cumulative frequency diagram If not an unambiguous unique line or point, i.e. not clearly labelled in working or on the graph, allow for a line (or point) indicated that is not the least or greatest value shown Only if B1 B1 B1 awarded, penalise -1 if a correct format for a box-and-whisker diagram is not shown

Mark scheme (b)

Scheme	Marks	Comments
(i) 0.75 × 68 or equivalent	M1
51 (yachts)	A1	Answer space takes precedence If no marks, award SC1 for sight of 17 (from 0.25 × 68)
(ii) Conclusion ‘Eog’ with sight of (Eog IQR 20 – 5 =) 15 (m) AND (Clwyd IQR 18 – 10 =) 8 (m)	B2	FT ‘their UQ – LQ’ from (a) box-and–whisker diagram B1 for either IQR correct
(iii) Conclusion ‘Can’t tell’ with reason, e.g. ‘only know that 25% of yachts in Clwyd Marina are greater than 18m’ ‘we don’t know if any of the yachts in Clwyd Marina are greater than 22(metres, the longest in Eog Marina)’ ‘we don’t know if a yacht in Clwyd Marina is greater than 22(metres)’ ‘it doesn’t say maximum length of Clwyd Marina’s results’	E1	Ignore any additional incorrect or spurious statements Allow ‘Can’t tell’ with a reason, e.g. ‘no raw data’ ‘don’t know this information’ ‘doesn’t show anywhere the biggest yacht in Clwyd Marina’ ‘we are only given some of the lengths of the yachts in the marinas’ ‘doesn’t show Clwyd Marina’s results’ ‘not specified’ ‘not specific’ ‘range not given for the Clwyd Marina (so can’t identify the longest yacht)’ Do not accept, e.g. ‘don’t know how many yachts in the marinas’ ‘not mentioned for either marina’