ECZ 2018 · GCE Paper 2 · Question 11 — Statistics
A farmer planted 60 fruit trees. In a certain month, the number of fruits per tree was recorded and the results were as shown in the table below. Fruits per tree2345678Frequency1546101618
(a) Calculate the standard deviation.[6]
Verified working — step 1
x = fruits, f = frequency: sum f = 60.(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. Fruits per tree2345678Cumulative Frequency161016264260Relative cumulative frequency0.020.10.170.27[1]
Verified working — step 1
Relative cumulative frequency = cumulative frequency60.(b(ii)) Using a scale of 1 cm to represent 1 unit on the x-axis for 0 ≤ x ≤ 8 and 2 cm to represent 0.1 units on the y-axis for 0 ≤ y ≤ 1, draw a smooth relative cumulative frequency curve.[3]
Verified working — step 1
Scale: x-axis 1 cm to 1 unit (0 to 8), y-axis 2 cm to 0.1 unit (0 to 1).(b(iii)) Showing your method clearly, use your graph to estimate the 70th percentile.[2]
Verified working — step 1
The 70th percentile sits at relative cumulative frequency 0.70.The full step-by-step working and final answer are included with Premium — checked against ECZ marking standards.
Original examination question © Examinations Council of Zambia. Worked solution and commentary © G12 Titan — not to be reproduced without permission.
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