ECZ 2023 · GCE Paper 2 · Question 11 — Statistics
The ages (in years) of 100 patients treated at a certain health centre on a particular day are given in the table below. Age in years0 < x ≤ 1010 < x ≤ 2020 < x ≤ 3030 < x ≤ 4040 < x ≤ 5050 < x ≤ 60Number of patients51025302010
(a) Calculate the standard deviation.[6]
Verified working — step 1
Midpoints x: 5, 15, 25, 35, 45, 55 with f: 5, 10, 25, 30, 20, 10 (N = 100).(b) Answer this part of the question on a sheet of graph paper.
(b(i)) Using the table above, copy and complete the cumulative frequency table below. Age in years≤ 0≤ 10≤ 20≤ 30≤ 40≤ 50≤ 60Number of patients0515100[1]
Verified working — step 1
Add each class frequency to the running total:(b(ii)) Using a scale of 2 cm to represent 10 units on each axis for 0 ≤ x ≤ 60 and 0 ≤ y ≤ 100, draw a smooth cumulative frequency curve.[3]
Verified working — step 1
Plot cumulative frequency at each UPPER class boundary:(b(iii)) Showing your method clearly, use your graph to estimate the semi-interquartile range.[2]
Verified working — step 1
Quartile positions: Q1 at 25 and Q3 at 75 on the cumulative axis.The full step-by-step working and final answer are included with Premium — checked against ECZ marking standards.
Original examination question © Examinations Council of Zambia. Worked solution and commentary © G12 Titan — not to be reproduced without permission.
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