ECZ 2023 · GCE Paper 2 · Question 11 — Statistics

The table shows the ages in years of 100 patients treated at a certain health centre on a particular day. Age0<x≤1010<x≤2020<x≤3030<x≤4040<x≤5050<x≤60Number of patients51025302010 The cumulative frequency table is given below, with some values left blank. Age≤0≤10≤20≤30≤40≤50≤60Cumulative frequency0515100

(a) Calculate the standard deviation.[6]

Verified working — step 1

Use midpoints x and frequencies f:

(b(i)) Copy and complete the cumulative frequency table (values for ≤30, ≤40 and ≤50).[1]

Verified working — step 1

Add frequencies successively to the previous cumulative total:

(b(ii)) Using a scale of 2cm to represent 10 units on each axis for 0 ≤ x ≤ 60 and 0 ≤ y ≤ 100, draw a smooth cumulative frequency curve.[3]

Verified working — step 1

On graph paper, using a scale of 2 cm : 10 units on both axes:

(b(iii)) Showing your method clearly, use your graph to estimate the semi-interquartile range.[2]

Verified working — step 1

From the ogive:

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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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