ECZ 2022 · GCE Paper 2 · Question 10 — Statistics
The frequency distribution table shows the number of hours students studied on a particular day at a college. Number of hours1234567Number of students0335621
(a) Calculate the standard deviation.[6]
Verified working — step 1
Use the hours as x with f their frequencies (N = 20).(b) Answer this part of the question on a sheet of graph paper.
(b(i)) Using the table above, copy and complete the relative cumulative frequency table below. Number of hours≤ 1≤ 2≤ 3≤ 4≤ 5≤ 6≤ 7Cumulative frequency03611171920Relative cumulative frequency00.150.30.55[1]
Verified working — step 1
Relative cumulative frequency = …(b(ii)) Using a scale of 2 cm to represent 1 unit on the x-axis for 0 ≤ x ≤ 7 and 2 cm to represent 0.1 units on the y-axis for 0 ≤ y ≤ 1, draw a smooth relative cumulative frequency curve.[3]
Verified working — step 1
Plot each x against its relative cumulative frequency:(b(iii)) Showing your method clearly, use your graph to estimate the 40th percentile.[2]
Verified working — step 1
The 40th percentile sits at relative cumulative frequency 0.40.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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