ECZ 2017 · GCE Paper 2 · Question 8 — Statistics

The frequency table below shows the number of copies of newspapers allocated to 48 newspaper vendors. Copies of newspapers25 < x ≤ 3030 < x ≤ 3535 < x ≤ 4040 < x ≤ 4545 < x ≤ 5050 < x ≤ 5555 < x ≤ 60Number of vendors547111281

(a) Calculate the standard deviation.[6]

Verified working — step 1

Midpoints x: 27.5, 32.5, 37.5, 42.5, 47.5, 52.5, 57.5 with f: 5, 4, 7, 11, 12, 8, 1 (sum f = 48).

(b) Answer this part of the question on a sheet of graph paper.

(b(i)) Using the information in the table above, copy and complete the cumulative frequency table below. Copies of newspapers≤ 25≤ 30≤ 35≤ 40≤ 45≤ 50≤ 55≤ 60Number of vendors0591627[1]

Verified working — step 1

Add each class frequency to the running total.

(b(ii)) Using a horizontal scale of 2 cm to represent 10 newspapers on the x-axis for 0 ≤ x ≤ 60 and a vertical scale of 4 cm to represent 10 vendors on the y-axis for 0 ≤ y ≤ 50, draw a smooth cumulative frequency curve.[3]

Verified working — step 1

Scale: x-axis 2 cm to 10 newspapers (0 to 60), y-axis 4 cm to 10 vendors (0 to 50).

(b(iii)) Showing your method clearly, use your graph to estimate the 50th percentile.[2]

Verified working — step 1

The 50th percentile is at half the total: 0.5 × 48 = 24.

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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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