Question
200 people were asked the amount of time T (minutes) they had spent in the supermarket. The results are represented in the table below.
a.State if the data is discrete or continuous.[1]
b.State the modal group.[1]
c.Write down the midpoint of the interval 10 < T ≤ 20 .[1]
d.Use your graphic display calculator to find an estimate for
(i) the mean;
(ii) the standard deviation.[3]
e.The results are represented in the cumulative frequency table below, with upper class boundaries of 10, 20, 30, 40, 50.
Write down the value of
(i) q;
(ii) r.[2]
f.The results are represented in the cumulative frequency table below, with upper class boundaries of 10, 20, 30, 40, 50.
On graph paper, draw a cumulative frequency graph, using a scale of 2 cm to represent 10 minutes (T) on the horizontal axis and 1 cm to represent 10 people on the vertical axis.[4]
g.Use your graph from part (f) to estimate
(i) the median;
(ii) the 90th percentile of the results;
(iii) the number of people who shopped at the supermarket for more than 15 minutes.[6]
▶️Answer/Explanation
Markscheme
continuous (A1)[1 mark]
20 < T ≤ 30 (A1)[1 mark]
15 (A1)[1 mark]
(i) 21.5 (G2)
(ii) 9.21 (9.20597…) (G1) [3 marks]
(i) q = 194 (A1)
(ii) r = 200 (A1)[2 marks]