ECZ 2016 · GCE Paper 2 · Question 8 — Statistics
Answer the whole of this question on a sheet of graph paper. A farmer had 260 potatoes in a sack. The masses, in grams, of the potatoes are given in the table below. Mass x grams100 < x ≤ 150150 < x ≤ 200200 < x ≤ 250250 < x ≤ 300300 < x ≤ 350350 < x ≤ 400No. of Potatoes15457580405
(a) Calculate an estimate of the mean mass of the potatoes.[3]
Verified working — step 1
Midpoints x: 125, 175, 225, 275, 325, 375 with f: 15, 45, 75, 80, 40, 5.(b(i)) Copy and complete the cumulative frequency table below. Mass x grams≤ 100≤ 150≤ 200≤ 250≤ 300≤ 350≤ 400Cumulative frequency01560260[1]
Verified working — step 1
Add each class frequency to the running total.(b(ii)) Using a horizontal scale of 2 cm to represent 50 grams for masses between 0 and 400 grams and a vertical scale of 2 cm to represent 25 potatoes, draw a smooth cumulative frequency curve.[3]
Verified working — step 1
Scale: horizontal 2 cm to 50 g (0 to 400), vertical 2 cm to 25 potatoes.(b(iii)) Use your graph to find
(b(iii)(a)) the median,[1]
Verified working — step 1
The median sits at N2 = 2602 = 130.(b(iii)(b)) the interquartile range.[2]
Verified working — step 1
Quartiles sit at N4 = 65 and 3N4 = 195.(c) A potato is picked at random from the sack. What is the probability that it has a mass greater than 250 grams?[2]
Verified working — step 1
From the table, 135 potatoes have mass 250 g or less.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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