ECZ 2018 · O-Level Paper 2 · Question 9 — Statistics

The frequency table below shows the distribution of marks obtained by 90 learners on a test. Marks10<x≤2020<x≤3030<x≤4040<x≤5050<x≤6060<x≤70Frequency21015233010

(a) Calculate the standard deviation.[6]

Verified working — step 1

Midpoints x: 15, 25, 35, 45, 55, 65 with f: 2, 10, 15, 23, 30, 10.

(b(i)) Copy and complete the relative cumulative frequency table. Marks≤10≤20≤30≤40≤50≤60≤70Cumulative frequency021227508090Relative cumulative frequency00.020.130.3[1]

Verified working — step 1

Relative cumulative frequency = …

(b(ii)) Using a scale of 2 cm to represent 10 units on the x-axis for 0 <= x <= 70 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 upper class boundary against its relative…

(b(iii)) Showing your method clearly, use your graph to estimate the 65th percentile.[2]

Verified working — step 1

The 65th percentile is read at a relative cumulative frequency of 0.65.

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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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