ECZ 2026 · GCE Paper 2 · Question 9 — Statistics
The frequency table shows the distribution by age of 70 people in a town. Age years0 < x ≤ 1010 < x ≤ 2020 < x ≤ 3030 < x ≤ 4040 < x ≤ 5050 < x ≤ 60Frequency4161820102
(a) Calculate the standard deviation.[6]
Verified working — step 1
Use class midpoints x: 5, 15, 25, 35, 45, 55 with f: 4, 16, 18, 20, 10, 2 (sum f = 70).(b(i)) Using the information in the frequency table, complete the following relative cumulative frequency table. Age years≤ 0≤ 10≤ 20≤ 30≤ 40≤ 50≤ 60Cumulative frequency042038586870Relative cumulative frequency0.000.060.290.54[1]
Verified working — step 1
Relative cumulative frequency = cumulative frequencytotal (70):(b(ii)) Using a scale of 2cm to represent 10 units on the x-axis for 0 ≤ x ≤ 60 and 2cm to represent 0.1 unit on the y-axis for 0 ≤ y ≤ 1, draw a smooth relative cumulative frequency curve.[3]
Verified working — step 1
Plot relative cumulative frequency at each UPPER class boundary:(b(iii)) Showing your method clearly, use your graph to estimate the interquartile range.[2]
Verified working — step 1
On a relative scale the quartiles sit at 0.25 and 0.75.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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