ECZ 2020 · O-Level Paper 2 · Question 9 — Statistics
The table below shows the distribution of lengths of plots in a certain locality. Length of plot in m1≤x≤56≤x≤1011≤x≤1516≤x≤2021≤x<2526≤x<3031≤x≤35Frequency0211443184
(a) Calculate the standard deviation.[6]
Verified working — step 1
Midpoints x: 3, 8, 13, 18, 23, 28, 33 with f: 0, 2, 11, 44, 31, 8, 4 (N = 100).(b(i)) Using the table above, copy and complete the cumulative frequency table below. Length of plot in m≤5≤10≤15≤20≤25≤30≤35Frequency0213100[1]
Verified working — step 1
Add each class frequency to the running total:(b(ii)) Using a scale of 2 cm to represent 5 units on the horizontal axis and 2 cm to represent 10 units on the vertical axis, 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 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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