ECZ 2018 · GCE Paper 2 · Question 11 — Statistics

A farmer planted 60 fruit trees. The table shows the number of fruits per tree. Number of fruits2345678Number of trees1546101618 The cumulative and relative cumulative frequency table is given below, with some values left blank. Number of fruits≤2≤3≤4≤5≤6≤7≤8Cumulative frequency161016Relative cumulative frequency0.020.10.170.27

(a) Calculate the standard deviation.[6]

Verified working — step 1

Use x=number of fruits, f=frequency.

(b(i)) Copy and complete the relative cumulative frequency table (values for 6, 7 and 8 fruits).[1]

Verified working — step 1

Cumulative frequencies:

(b(ii)) Draw a smooth relative cumulative frequency curve (1cm = 1 unit on x, 2cm = 0.1 on y).[3]

Verified working — step 1

Plot the points (x, relative c.f.) using the upper class boundaries: (2,0.02), (3,0.10), (4,0.17), (5,0.27), (6,0.43), (7,0.70), (8,1.00).

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

Verified working — step 1

The 70th percentile corresponds to 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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