ECZ 2024 · GCE Paper 2 · Question 11 — Statistics
The frequency table shows the marks obtained by 50 learners in a Mathematics test. Marks10<x≤2020<x≤3030<x≤4040<x≤5050<x≤6060<x≤7070<x≤80Number of learners371215832 The cumulative frequency table is given below, with some values left blank. Marks≤10≤20≤30≤40≤50≤60≤70≤80Cumulative frequency03102250
(a) Calculate the standard deviation.[6]
Verified working — step 1
Use midpoints x of each class:(b(i)) Copy and complete the cumulative frequency table (values for ≤50, ≤60 and ≤70).[1]
Verified working — step 1
Add each class frequency to the previous cumulative total:(b(ii)) Using a scale of 2cm to represent 10 marks on the x-axis for 0 ≤ x ≤ 80 and 2cm to represent 5 units on the y-axis for 0 ≤ y ≤ 50, draw a smooth cumulative frequency curve.[3]
Verified working — step 1
Plot the cumulative frequency points at the upper class boundaries:(b(iii)) Showing your method clearly, use your graph to estimate the 70th percentile.[2]
Verified working — step 1
70th percentile position = (70100) × 50 = 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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