ECZ 2025 · GCE Paper 2 · Question 7 — Statistics
The frequency distribution table shows the amount of money spent by customers at a particular shop. Amount K0 < x ≤ 2020 < x ≤ 4040 < x ≤ 6060 < x ≤ 8080 < x ≤ 100Frequency52055182
(a) Calculate the standard deviation.[6]
Verified working — step 1
Use class midpoints x: 10, 30, 50, 70, 90 with f: 5, 20, 55, 18, 2 (N = 100).(b(i)) Using the information in the frequency distribution table, complete the cumulative frequency table below. Amount K≤ 0≤ 20≤ 40≤ 60≤ 80≤ 100Cumulative frequency05100[1]
Verified working — step 1
Each entry adds the next class frequency to the running total:(b(ii)) Using a horizontal scale of 2 cm to represent 20 units on the x-axis for 0 ≤ x ≤ 100 and a vertical scale of 2 cm to represent 10 units on the y-axis for 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 on the cumulative axis: Q1 at N4 = 25 and Q3 at 3N4 = 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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