ECZ 2025 · GCE Paper 2 · Question 7 — Statistics
The frequency distribution table shows the amount of money spent by customers at a particular shop. Amount spent0<x≤2020<x≤4040<x≤6060<x≤8080<x≤100Number of customers52055182 The cumulative frequency table is given below, with some values left blank. Amount spent≤0≤20≤40≤60≤80≤100Cumulative frequency05100
(a) Calculate the standard deviation.[6]
Verified working — step 1
Use midpoints of each class:(b(i)) Using the information in the frequency distribution table, complete the cumulative frequency table (values for ≤40, ≤60 and ≤80).[1]
Verified working — step 1
Add frequencies cumulatively:(b(ii)) Using a horizontal scale of 2cm to represent 20 units on the x-axis for 0 ≤ x ≤ 100 and a vertical scale of 2cm to represent 10 units on the y-axis for 0 ≤ y ≤ 100, draw a smooth cumulative frequency curve.[3]
Verified working — step 1
Plot the cumulative frequency points at the upper class boundaries:(b(iii)) Showing your method clearly, use your graph to estimate the semi-interquartile range.[2]
Verified working — step 1
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Original examination question © Examinations Council of Zambia. Worked solution and commentary © G12 Titan — not to be reproduced without permission.
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