ECZ 2013 · O-Level Paper 2 · Question 12 — Statistics
The table shows the number of litres of water that 80 pupils at Tapasa Primary School drank on two cold days. Litres of water x0 < x ≤ 0.50.5 < x ≤ 11 < x ≤ 1.51.5 < x ≤ 22 < x ≤ 2.52.5 < x ≤ 33 < x ≤ 3.53.5 < x ≤ 4Number of pupils22719301451
(a) Calculate the estimated mean litres of water drank.[3]
Verified working — step 1
Midpoints: 0.25, 0.75, 1.25, 1.75, 2.25, 2.75, 3.25, 3.75.(b) Copy and complete the cumulative frequency distribution. Litres of water x≤0≤0.5≤1≤1.5≤2≤2.5≤3≤3.5≤4Frequency0241130[2]
Verified working — step 1
Add each class frequency to the running total.(c) Using a horizontal scale of 4 cm to represent 1 litre of water on the x-axis and a vertical scale of 2 cm to represent 10 pupils on the y-axis, draw a smooth cumulative frequency curve.[3]
Verified working — step 1
Scale: horizontal 4 cm to 1 litre, vertical 2 cm to 10 pupils.(d) Showing your method clearly, use your graph to estimate
(d(i)) the median,[1]
Verified working — step 1
The median sits at 802 = 40.(d(ii)) the interquartile range,[2]
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Quartiles sit at 804 = 20 and 3 × 804 = 60.(d(iii)) the 80th percentile.[1]
Verified working — step 1
The 80th percentile sits at 0.80 × 80 = 64.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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