ECZ 2017 · GCE Paper 2 · Question 8 — Statistics

The table shows the number of copies allocated to 48 newspaper vendors. Copies allocated25<x≤3030<x≤3535<x≤4040<x≤4545<x≤5050<x≤5555<x≤60Number of vendors547111281

(a) Calculate the standard deviation.[6]

Verified working — step 1

Use class midpoints x and frequencies f:

(b(i)) Copy and complete the cumulative frequency table. Copies allocated≤25≤30≤35≤40≤45≤50≤55≤60Cumulative frequency0591627[1]

Verified working — step 1

Add frequencies cumulatively using upper class boundaries:

(b(ii)) Draw a smooth cumulative frequency curve (2cm = 10 newspapers on x, 4cm = 10 vendors on y).[3]

Verified working — step 1

Plot the cumulative frequency (y-axis) against the upper class boundary (x-axis) for each class:

(b(iii)) Showing your method clearly, use your graph to estimate the 50th percentile.[2]

Verified working — step 1

The 50th percentile corresponds to the value of x for which the cumulative frequency = 50% of 48 = 24.

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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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