ECZ 2016 · GCE Paper 2 · Question 8 — Statistics
Answer on graph paper. The table shows 260 potatoes grouped by mass, in grams. Mass in grams100<x≤150150<x≤200200<x≤250250<x≤300300<x≤350350<x≤400Frequency15457580405
(a) Calculate an estimate of the mean mass of the potatoes.[3]
Verified working — step 1
Use class midpoints × frequency:(b(i)) Copy and complete the cumulative frequency table.[1]
Verified working — step 1
Cumulative frequencies:(b(ii)) Draw a smooth cumulative frequency curve.[3]
Verified working — step 1
Plot cumulative frequency against upper class boundary: (100,0),(150,15),(200,60),…(b(iii)(a)) Use your graph to find the median.[1]
Verified working — step 1
Median at N2= …(b(iii)(b)) Use your graph to find the interquartile range.[2]
Verified working — step 1
Lower quartile at N4= 65th value ≈ 205 g; upper quartile at 3N4= …(c) Probability that a potato has mass greater than 250 grams.[2]
Verified working — step 1
Number with mass ≤ 250 g = 135. Number > 250 g = 260 − 135 = …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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