ECZ 2019 · GCE Paper 2 · Question 9 — Statistics
The table shows the ages of 30 football players. Age10111213141516Number of players0257862 The cumulative and relative cumulative frequency table is given below, with some values left blank. Age≤10≤11≤12≤13≤14≤15≤16Cumulative frequency02714222830Relative cumulative frequency0.000.070.231.00
(a) Calculate the standard deviation.[6]
Verified working — step 1
Mean = Σfx/Σf = 10×0+11×2+12×5+13×7+14×8+15×6+16×230(b(i)) Copy and complete the relative cumulative frequency table (values for ≤13, ≤14 and ≤15).[1]
Verified working — step 1
Relative cumulative frequency = cumulative frequency ÷ 30(b(ii)) Draw a smooth relative cumulative frequency curve (2cm = 1 unit on x for 10 ≤ x ≤ 16; 2cm = 0.1 on y).[3]
Verified working — step 1
Plot the ages (10,11,12,13,14,15,16) on the x-axis using a scale of 2 cm = 1 unit, and the relative cumulative frequencies (0.00, 0.07, 0.23, 0.47, 0.73, 0.93, 1.00) on the y-axis using a scale of 2 cm = 0.1 unit.(b(iii)) Showing your method clearly, use your graph to estimate the 90th percentile.[2]
Verified working — step 1
To find the 90th percentile, locate 0.90 on the y-axis (relative cumulative frequency axis).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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