ECZ 2024 · GCE Paper 2 · Question 11 — Statistics
The frequency table shows the distribution of marks obtained by 50 learners in a Mathematics test. Marks x10 < x ≤ 2020 < x ≤ 3030 < x ≤ 4040 < x ≤ 5050 < x ≤ 6060 < x ≤ 7070 < x ≤ 80Frequency371215832
(a) Calculate the standard deviation.[6]
Verified working — step 1
Midpoints x: 15, 25, 35, 45, 55, 65, 75 with f: 3, 7, 12, 15, 8, 3, 2 (N = 50).(b) Answer this part of the question on a sheet of graph paper.
(b(i)) Using the information in the table above, copy and complete the cumulative frequency table below. Marks x≤ 10≤ 20≤ 30≤ 40≤ 50≤ 60≤ 70≤ 80Cumulative frequency03102250[1]
Verified working — step 1
Add each class frequency to the running total:(b(ii)) Using a scale of 2 cm to represent 10 marks on the x-axis for 0 ≤ x ≤ 80 and 2 cm to represent 5 units on the y-axis for 0 ≤ y ≤ 50, 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 70th percentile.[2]
Verified working — step 1
70th percentile position: (70100) x 50 = the 35th value.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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