ECZ 2010 · O-Level Paper 2 · Question 10 — Statistics
The following table shows the total number of points scored by 110 candidates at Mingule High School, in the 2007 Grade 12 Final Examinations. Points scored6 < x ≤ 88 < x ≤ 1010 < x ≤ 1212 < x ≤ 1414 < x ≤ 1616 < x ≤ 20Frequency13169152235
(a) Calculate the estimated mean points scored.[2]
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Midpoints: 7, 9, 11, 13, 15, 18.(b) Copy and complete the table showing the cumulative frequency distribution. Points scored≤6≤8≤10≤12≤14≤16≤20Frequency013110[2]
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Add each class frequency to the running total.(c) Using a horizontal scale of 2 cm to represent 2 points and a vertical scale of 2 cm to represent 10 candidates, draw a smooth cumulative frequency curve.[3]
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Scale: horizontal 2 cm to 2 points, vertical 2 cm to 10 candidates.(d) Use your graph to find the median points scored.[2]
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The median sits at 1102 = 55.(e) A scholarship was offered to two candidates. Find the probability that the two candidates chosen scored less than 14 points.[2]
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53 of the 110 candidates scored less than 14 points.(f) Selection to the University of Zambia was done and only those who scored 14 points or less were selected. How many candidates were not selected from this group?[1]
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53 candidates scored 14 points or less and were selected.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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