ECZ 2021 · O-Level Paper 2 · Question 10 — Statistics

The table below shows the heights of trees in a plantation. Height in cm0<x≤1010<x≤2020<x≤3030<x≤4040<x≤5050<x≤6060<x≤70Frequency30702002001603010

(a) Calculate the standard deviation.[6]

Verified working — step 1

Midpoints x: 5, 15, 25, 35, 45, 55, 65 with f: 30, 70, 200, 200, 160, 30, 10.

(b(i)) Using the table above, copy and complete the relative cumulative frequency table. Height in cm≤0≤10≤20≤30≤40≤50≤60≤70Cumulative frequency030100300500660690700Relative cumulative frequency0.000.040.140.431.00[1]

Verified working — step 1

Divide each cumulative fr…

(b(ii)) Using a scale of 2 cm to represent 10 units on the x-axis for 0 <= x <= 70 and 2 cm to represent 0.1 units on the y-axis for 0.00 <= y <= 1.00, draw a smooth relative cumulative frequency curve.[3]

Verified working — step 1

Plot each upper class boundary against its relative cumu…

(b(iii)) Showing your method clearly, use your graph to estimate the 80th percentile.[2]

Verified working — step 1

The 80th percentile is read at a relative cumulative frequency of 0.80.

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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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