ECZ 2024 · O-Level Paper 2 · Question 8 — Statistics

The table shows the time, in minutes, taken by 80 learners to complete a task in a Science experiment. Time in minutes0<x≤22<x≤44<x≤66<x≤88<x≤1010<x≤12Number of learners5152520105

(a) Calculate the standard deviation.[6]

Verified working — step 1

Midpoints x: 1, 3, 5, 7, 9, 11 with f: 5, 15, 25, 20, 10, 5 (N = 80).

(b(i)) Using the table above, copy and complete the cumulative frequency table below. Time in minutes≤0≤2≤4≤6≤8≤10≤12Number of learners052045[1]

Verified working — step 1

Keep adding each class frequency to the running total:

(b(ii)) Using a scale of 2 cm to represent 2 units on the x-axis for 0 ≤ x ≤ 12 and 2 cm to represent 10 units on the y-axis for 0 ≤ y ≤ 80, 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 semi-interquartile range.[2]

Verified working — step 1

With n = 80: Q1 sits at cumulative frequency 20 and Q3 at 60.

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Original examination question © Examinations Council of Zambia. Worked solution and commentary © G12 Titan — not to be reproduced without permission.

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