Box Plots: Eduqas GCSE Higher November 2021 Paper 1 Q15

Higher November 2021 Paper 1 Q15

EduqasHigherCurrent spec8 marksBox Plots Cumulative Frequency

15. The owner of a double glazing company employs 50 salespeople.
For the month of June 2019, the total sales made by each salesperson is recorded in the table.

Sales, \(s\) (thousand pounds)	\(10 \lt s \leqslant 20\)	\(20 \lt s \leqslant 30\)	\(30 \lt s \leqslant 40\)	\(40 \lt s \leqslant 50\)	\(50 \lt s \leqslant 60\)
Frequency	0	8	15	18	9

(a) Complete the following cumulative frequency table. [1]

Sales, \(s\) (thousand pounds)	\(s \leqslant 20\)	\(s \leqslant 30\)	\(s \leqslant 40\)	\(s \leqslant 50\)	\(s \leqslant 60\)
Cumulative frequency	0	8

(b) On the grid below, draw a cumulative frequency diagram to show these results. [3]

Blank grid titled Sales for June 2019: cumulative frequency from 0 to 50 (up to 55) against sales, s (thousand pounds), from 10 to 60 (up to 65)

	Bonus
Top 10% of salespeople	Gold
Next 20% of salespeople	Silver

(i) Use your graph to find the minimum value of sales needed to earn each bonus in June 2019. [2]

Gold bonus £ ………………………… Silver bonus £ …………………………

(ii) Explain why your answers to part (c)(i) may not be accurate. [1]

(d) The box plot shows summary statistics for the month of September 2019.

Box plot on a sales axis, s (thousand pounds), from 10 to 60: minimum 20, lower quartile 33, median 35, upper quartile 48, maximum 59

The owner is considering closing the business for 2 days of staff training next year.
This can take place in either June or September.

Using the sales data from 2019, should the owner choose to train her staff in June or September?

June ☐ September ☐

Show how you decide. [1]

Scheme	Marks	Comments
23 41 50	B1

Mark scheme (b)

Scheme	Marks	Comments
5 points plotted correctly: (20, 0) (30, 8) (40, 23) (50, 41) (60, 50)	B2	FT ‘their cf’ provided cumulative; tolerance ± 1mm B1 for 3 or 4 correct plots
All points joined with a smooth curve or with line segments	B1	dep on at least B1 for plots; last point must not be joined to the axis; tolerance ± 1mm

Mark scheme (c)

Scheme	Marks	Comments
(c)(i) Gold bonus: Answer in range 53 000 to 55 000 inclusive Silver bonus: Answer in range 45 000 to 47 000 inclusive	B2	FT their cf graph for ‘their s’ when cf is 45 and 35 B1 FT for each If no marks, award SC1 for both Gold bonus in range 53 to 55 and Silver bonus in range 45 to 47
(c)(ii) Valid explanation e.g. ‘The data may not be evenly spread through each group.’ or ‘All the sales in the group 50 to 60 may be 60 000.’ or ‘The raw data is not used.’	E1	Allow e.g. ‘It is estimated because the data is grouped.’ or ‘Because you do not know what each salesperson got.’