ECZ 2025 · O-Level Paper 2 · Question 10 — Statistics
The frequency table shows the heights of mango seedlings measured and recorded on a particular day. Height in cm0<x≤44<x≤88<x≤1212<x≤1616<x≤2020<x≤2424<x≤28Frequency21120243184
(a) Calculate the standard deviation.[6]
Verified working — step 1
Use class midpoints x: 2, 6, 10, 14, 18, 22, 26 with f: 2, 11, 20, 24, 31, 8, 4.(b(i)) Using the information in the frequency table, complete the following relative cumulative frequency table. Height in cm≤0≤4≤8≤12≤16≤20≤24≤28Cumulative frequency021333578896100Relative cumulative frequency00.020.131[1]
Verified working — step 1
Relative cumulative frequency = …(b(ii)) Using a scale of 2 cm to represent 4 units on the x-axis and 2 cm to represent 0.1 units on the y-axis, draw a smooth relative cumulative frequency curve.[3]
Verified working — step 1
Plot each UPPER class boundary against its relative cumulative frequency:(b(iii)) Showing your method clearly, use your graph to estimate the 60th percentile.[2]
Verified working — step 1
The 60th percentile sits at relative cumulative frequency 0.60.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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