ECZ 2019 · O-Level Paper 2 · Question 8 — Statistics
The table below shows the expenditure of 90 farmers in a particular farming season. Amount in K0<x≤100100<x≤200200<x≤300300<x≤400400<x≤500500<x≤600600<x≤700700<x≤800Number of farmers5161717141272
(a) Calculate the standard deviation.[6]
Verified working — step 1
Midpoints x: 50, 150, 250, 350, 450, 550, 650, 750 with f: 5, 16, 17, 17, 14, 12, 7, 2 (N = 90).(b(i)) Using the table above, copy and complete the cumulative frequency table below. Amount in K≤0≤100≤200≤300≤400≤500≤600≤700≤800Frequency0521385569[1]
Verified working — step 1
Add each class frequency to the running total:(b(ii)) Using a scale of 2 cm to represent 100 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 = 90: Q1 at cumulative frequency 22.5 and Q3 at 67.5.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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