ECZ 2015 · O-Level Paper 2 · Question 9 — Statistics
On a particular day, a tuck shop owner recorded the expenditure of 350 boys and the results were as shown in the table below. Amount K10<x≤2020<x≤3030<x≤4040<x≤5050<x≤6060<x≤7070<x≤8080<x≤9090<x≤100Number of boys20505570604535105
(a) Calculate the mean amount of money spent.[3]
Verified working — step 1
Midpoints: 15, 25, 35, 45, 55, 65, 75, 85, 95.(b) Copy and complete the cumulative frequency distribution. Amount K≤10≤20≤30≤40≤50≤60≤70≤80≤90≤100Number of boys02070125195255300350[1]
Verified working — step 1
Add each class frequency to the running total.(c) Using a horizontal scale of 2 cm to represent K10.00 and a vertical scale of 2 cm to represent 50 boys, draw a smooth cumulative frequency curve.[3]
Verified working — step 1
Scale: horizontal 2 cm to K10, vertical 2 cm to 50 boys.(d) Showing your method clearly, use your graph to estimate
(d(i)) the median,[1]
Verified working — step 1
The median is the 175th value (3502).(d(ii)) the semi-interquartile range.[2]
Verified working — step 1
Quartiles sit at n4 = 87.5 and 3n4 = 262.5.(e) Given that those who spent K75.00 or more qualified for a draw in a competition to win a prize, find the number of boys who qualified for the draw.[2]
Verified working — step 1
K75 sits halfway through the 70 to 80 class, so half its 35 boys qualify: 17.5.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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