ECZ 2021 · GCE Paper 2 · Question 9 — Statistics

The table shows the results obtained by 60 learners in a mathematics test. Marks scored0<x≤1010<x≤2020<x≤3030<x≤4040<x≤5050<x≤6060<x≤7070<x≤80Number of learners26101512843 The cumulative frequency table is given below, with some values left blank. Marks≤0≤10≤20≤30≤40≤50≤60≤70≤80Cumulative frequency028183345

(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 ≤60, ≤70 and ≤80).[1]

Verified working — step 1

Add each class frequency to the previous cumulative total:

(b(ii)) Using a scale of 2cm to represent 10 units on both axes for 0 ≤ x ≤ 80 and 0 ≤ y ≤ 60, draw a smooth cumulative frequency curve.[3]

Verified working — step 1

Plot the cumulative frequency points (upper class boundary, cumulative frequency):

(b(iii)) Showing your method clearly, use your graph to estimate the 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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