10 Ana records the amount of money spent by 140 customers in her shop on one day.
Amount spent (£\(a\))
Frequency
\(0 \lt a \leqslant 5\)
35
\(5 \lt a \leqslant 10\)
42
\(10 \lt a \leqslant 15\)
20
\(15 \lt a \leqslant 20\)
18
\(20 \lt a \leqslant 30\)
14
\(30 \lt a \leqslant 50\)
11
(a) Draw a histogram to represent this information.
[4]
(b) Ana wants to offer a discount to the customers who spend the most money in her shop.
Voucher Save 10% when you spend more than £…
She wants to give the discount to approximately 25% of her customers.
Suggest a suitable amount of money for Ana to use on her voucher. Justify your decision. [4]
Mark scheme (a)
Answer
Marks
Part marks and guidance
Fds 7, 8.4, 4, 3.6, 1.4, 0.55
1
At least 3 correct; may be implied by height of 3 bars including one of the last two
Bars all of correct height
1
Tolerance 1 mm unless on gridlines
FT their scale. Heights may be indicated by a plotted point, stick etc
Ignore polygon lines
Bars all of correct width
1
Condone missing vertical lines if tops correct width
Vertical axis with consistent linear scale starting from 0 soi and labelled ‘Frequency density’ oe
1
B0 for scale 0 to 42 etc for frequency graph even if labelled frequency density
Accept abbreviations or an area key eg 1 cm\(^2\) = 5
Notes
(corrected from the printed mark scheme: “Frequency denisity” is a spelling slip for “Frequency density”.)
Mark scheme (b)
Answer
Marks
Part marks and guidance
Answer £17 to £18 inclusive with valid working and justification
4
M1 for 25% of 140 = 35 or 75% of 140 = 105
M1dep for identification of 15 to 20 soi
eg implied by frequencies 25 and 43 or 97 and 115 or by answer in range 15 to 20
A1 for answer £17 to £18 inclusive B1dep on M1M1A1 for justification
If 0 scored, then SC1 for an answer £15 to £20
Justification can be based on a calculation eg \(\frac{10}{18}\) of 15 to 20 bar or reasoning eg 18% spent £20 and 30/31% spent £15, so 25% is just over/about halfway.
