ECZ 2020 · GCE Paper 2 · Question 8 — Statistics
The frequency table below shows the mark distribution for 30 learners in a Mathematics test. Marks10 < x ≤ 1515 < x ≤ 2020 < x ≤ 2525 < x ≤ 3030 < x ≤ 3535 < x ≤ 4040 < x ≤ 4545 < x ≤ 50Number of Learners23356632
(a) Calculate the standard deviation.[6]
Verified working — step 1
Midpoints x: 12.5, 17.5, 22.5, 27.5, 32.5, 37.5, 42.5, 47.5 with f: 2, 3, 3, 5, 6, 6, 3, 2 (N = 30).(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 relative cumulative frequency table below. Marks≤ 15≤ 20≤ 25≤ 30≤ 35≤ 40≤ 45≤ 50Number of Learners2581319252830Relative cumulative frequency0.070.170.270.431[1]
Verified working — step 1
Relative cumulative frequency = …(b(ii)) Using a scale of 2 cm to represent 5 marks on the axis for 15 ≤ x ≤ 50 and a scale of 2 cm to represent 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 each UPPER class boundary against its relative cumulative frequency:(b(iii)) Showing your method clearly, use your graph to estimate the semi-interquartile range.[2]
Verified working — step 1
On the relative curve, Q1 is read at y = 0.25 and Q3 at y = 0.75.The full step-by-step working and final answer are included with Premium — checked against ECZ marking standards.
Original examination question © Examinations Council of Zambia. Worked solution and commentary © G12 Titan — not to be reproduced without permission.
Have a different question?
Search it — if it is from a past paper or a school mock, chances are we have it worked out, or one that uses the same method.
Search any past-paper question