ECZ 2022 · GCE Paper 2 · Question 10 — Statistics
The frequency distribution table shows the number of hours studied by students on a particular day at a college. Number of hours1234567Number of students0335621 The relative cumulative frequency table is given below, with some values left blank. Number of hours≤1≤2≤3≤4≤5≤6≤7Cumulative frequency03611171920Relative cumulative frequency00.150.30.55
(a) Calculate the standard deviation.[6]
Verified working — step 1
Mean = Σfxn= 1×0+2×3+3×3+4×5+5×6+6×2+7×120= 8420= 4.2(b(i)) Copy and complete the relative cumulative frequency table (values for ≤5, ≤6 and ≤7).[1]
Verified working — step 1
Relative cumulative frequency = cumulative frequency ÷ 20(b(ii)) Using a scale of 2cm to represent 1 unit on the x-axis for 0 ≤ x ≤ 7 and 2cm 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 the points (x, relative cumulative frequency): (1,0), (2,0.15), (3,0.30), (4,0.55), (5,0.85), (6,0.95), (7,1.00).(b(iii)) Showing your method clearly, use your graph to estimate the 40th percentile.[2]
Verified working — step 1
The 40th percentile corresponds to 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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