ECZ 2012 · O-Level Paper 2 · Question 8 — Statistics

In a Survey, 200 shoppers were asked how much they had spent at Gulani Super Market on a particular day. The results are shown in the table below. Amount in '000 of Kwacha0 < x ≤ 2020 < x ≤ 4040 < x ≤ 6060 < x ≤ 8080 < x ≤ 100100 < x ≤ 140Number of shoppers103248543620

(a) Write the modal class.[1]

Verified working — step 1

The modal class is the one with the highest frequency.

(b) Estimate the mean amount spent.[3]

Verified working — step 1

Midpoints: 10, 30, 50, 70, 90, 120.

(c) Copy and complete the following cumulative frequency table. Amount in '000 of Kwacha≤0≤20≤40≤60≤80≤100≤140Number of shoppers0104290[1]

Verified working — step 1

Add each class frequency to the running total.

(d) Using a scale of 2 cm to represent K20 000 on the horizontal axis and 2 cm to represent 20 shoppers on the vertical axis, draw a smooth cumulative frequency curve.[3]

Verified working — step 1

Scale: horizontal 2 cm to K20 000, vertical 2 cm to 20 shoppers.

(e) Showing your method clearly, use your graph to estimate the interquartile range.[2]

Verified working — step 1

Quartiles sit at 2004 = 50 and 3 × 2004 = 150.

(f) Given that shoppers who spent at least K110 000 qualified for entry into a raffle draw, estimate the number of those who qualified.[2]

Verified working — step 1

Read the cumulative frequency at 110 from the curve: about 185.

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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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