ECZ 2023 · O-Level Paper 2 · Question 12 — Statistics

The following table shows the age distribution of 30 people in a village. Age in years0<x≤1010<x≤2020<x≤3030<x≤4040<x≤5050<x≤60Frequency269742

(a) Calculate the standard deviation.[6]

Verified working — step 1

Midpoints x: 5, 15, 25, 35, 45, 55 with f: 2, 6, 9, 7, 4, 2.

(b(i)) Using the table above, copy and complete the relative cumulative frequency table. Age in years≤0≤10≤20≤30≤40≤50≤60Cumulative frequency02817242830Relative cumulative frequency0.000.070.271.00[1]

Verified working — step 1

Divide each cumulative f…

(b(ii)) Using a scale of 2 cm to represent 10 units on the horizontal axis and 2 cm to represent 0.1 units on the vertical axis for 0 <= x <= 60 and 0.0 <= y <= 1.0, draw a smooth relative cumulative frequency curve.[3]

Verified working — step 1

Plot each upper class boundary against its relative cumu…

(b(iii)) Showing your method clearly, use your graph to estimate the 70th percentile.[2]

Verified working — step 1

The 70th percentile is read at a relative cumulative frequency of 0.70.

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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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