ECZ 2020 · GCE Paper 2 · Question 8 — Statistics

The frequency table shows the marks obtained by 30 learners. Marks10<x≤1515<x≤2020<x≤2525<x≤3030<x≤3535<x≤4040<x≤4545<x≤50Frequency23356632 The relative cumulative frequency table is given below, with some values left blank. Marks≤15≤20≤25≤30≤35≤40≤45≤50Relative cumulative frequency0.070.170.270.431

(a) Calculate the standard deviation.[6]

Verified working — step 1

Use midpoints x and f, N=30.

(b(i)) Copy and complete the relative cumulative frequency table (values for ≤35, ≤40 and ≤45).[1]

Verified working — step 1

Find cumulative frequencies:

(b(ii)) Using a scale of 2cm to 5 marks on the x-axis for 15 ≤ x ≤ 50 and 2cm to 0.1 units on the y-axis for 0.0 ≤ y ≤ 1.0, draw a smooth relative cumulative frequency curve.[3]

Verified working — step 1

Plot the upper class boundaries (15,20,25,30,35,40,45,50) on the x-axis against their relative cumulative frequencies (0.07,0.17,0.27,0.43,0.63,0.83,0.93,1.00) on the y-axis, using t…

(b(iii)) Showing your method clearly, use your graph to estimate the semi-interquartile range.[2]

Verified working — step 1

From the ogive:

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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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