ECZ 2022 · O-Level Paper 2 · Question 10 — Statistics
The table shows the heights of 100 plants measured in centimetres on a particular day. Height in cm0<x≤1010<x≤2020<x≤3030<x≤4040<x≤5050<x≤6060<x≤70Frequency38142223228
(a) Calculate the standard deviation.[6]
Verified working — step 1
Midpoints x: 5, 15, 25, 35, 45, 55, 65 with f: 3, 8, 14, 22, 23, 22, 8 (N = 100).(b(i)) Using the table above, copy and complete the cumulative frequency table below. Height in cm≤0≤10≤20≤30≤40≤50≤60≤70Cumulative frequency031125100[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 both axes for 0 ≤ x ≤ 70 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
With n = 100: Q1 at cumulative frequency 25 and Q3 at 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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