ECZ 2021 · GCE Paper 2 · Question 9 — Statistics
The following table shows the results obtained by 60 learners in a mathematics test. Marks scored0 < x ≤ 1010 < x ≤ 2020 < x ≤ 3030 < x ≤ 4040 < x ≤ 5050 < x ≤ 6060 < x ≤ 7070 < x ≤ 80Number of learners26101512843
(a) Calculate the standard deviation.[6]
Verified working — step 1
Midpoints x: 5, 15, 25, 35, 45, 55, 65, 75 with f: 2, 6, 10, 15, 12, 8, 4, 3 (N = 60).(b) Answer this part of the question on a sheet of graph paper.
(b(i)) Using the table above, copy and complete the cumulative frequency table below. Marks scored≤ 0≤ 10≤ 20≤ 30≤ 40≤ 50≤ 60≤ 70≤ 80Number of learners028183345[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 ≤ 80 and 0 ≤ y ≤ 60, 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
Quartile positions: Q1 at N4 = 15 and Q3 at 3N4 = 45 on the cumulative axis.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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