Question 12:
Table 5 in the answer space shows the age distribution of 40 visitors to a hot spring on a particular day.
(a) Complete Table 5 in the answer space.
[3 marks]
Answer:
You must use BB or 2B pencils to answer this question.
(b) For this part of the question, use the graph paper provided on page 156.
Using a scale of 2 cm to 5 years on the horizontal axis and 2 cm to 5 visitors on the vertical axis, draw a cumulative histogram for the data. [4 marks]
(c)(i) On the graph in (b), draw an ogive. You may use a flexible curve rule. [1 mark]
(ii) Only visitors at the 70th percentile and above will be given a drink voucher.
Find the minimum age required to get the voucher.
[2 marks]
Answer:
(a)
(b), (c)(i)
(b) Both axes are drawn in the correct direction with a uniform scale for 29.5 x 64.5 and 0 y 40.
Seven bars are drawn correctly using the boundary values.
Cumulative histogram is drawn correctly using the given scale.
(c)(i) The ogive is correctly drawn on the cumulative histogram.
(c)(ii)
$$ \begin{aligned} &\text { 70% of the total frequency }\\ &\begin{aligned} & =\frac{70}{100} \times 40 \\ & =28 \end{aligned} \end{aligned} $$
P70 = 50.5. The minimum age of visitors eligible to receive a drink voucher is 50.5.
Table 5 in the answer space shows the age distribution of 40 visitors to a hot spring on a particular day.
(a) Complete Table 5 in the answer space.
[3 marks]
Answer:
You must use BB or 2B pencils to answer this question.
(b) For this part of the question, use the graph paper provided on page 156.
Using a scale of 2 cm to 5 years on the horizontal axis and 2 cm to 5 visitors on the vertical axis, draw a cumulative histogram for the data. [4 marks]
(c)(i) On the graph in (b), draw an ogive. You may use a flexible curve rule. [1 mark]
(ii) Only visitors at the 70th percentile and above will be given a drink voucher.
Find the minimum age required to get the voucher.
[2 marks]
Answer:
(a)
(b), (c)(i)
(b) Both axes are drawn in the correct direction with a uniform scale for 29.5 x 64.5 and 0 y 40.
Seven bars are drawn correctly using the boundary values.
Cumulative histogram is drawn correctly using the given scale.
(c)(i) The ogive is correctly drawn on the cumulative histogram.
(c)(ii)
$$ \begin{aligned} &\text { 70% of the total frequency }\\ &\begin{aligned} & =\frac{70}{100} \times 40 \\ & =28 \end{aligned} \end{aligned} $$
P70 = 50.5. The minimum age of visitors eligible to receive a drink voucher is 50.5.