ECZ 2019 · GCE Paper 2 · Question 9 — Statistics

The table below shows the distribution of the ages of 30 football players at a school. Age x years10111213141516Frequency0257862

(a) Calculate the standard deviation.[6]

Verified working — step 1

Mean = sumfxsum(f) = 40730 = 13.567.

(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. Age x years≤ 10≤ 11≤ 12≤ 13≤ 14≤ 15≤ 16Cumulative Frequency02714222830Relative cumulative frequency0.000.070.231.00[1]

Verified working — step 1

Relative cumulative frequency = cumulative frequency30.

(b(ii)) Using a scale of 2 cm to represent 1 unit on the x-axis for 10 ≤ x ≤ 16 and a scale of 2 cm to represent 0.1 units on the y-axis for 0.0 ≤ y ≤ 1.0, draw a smooth relative cumulative frequency curve.[3]

Verified working — step 1

Scale: x-axis 2 cm to 1 unit (10 to 16), y-axis 2 cm to 0.1 unit (0 to 1).

(b(iii)) Showing your method clearly, use your graph to estimate the 90th percentile.[2]

Verified working — step 1

The 90th percentile sits at relative cumulative frequency 0.90.

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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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