Theory question 112
Measures of DispersionThe table below shows the weekly profit in naira from a Mini-market.
Weekly profit (N): 1-10, 11-20, 21-30, 31-40, 40-50, 51-60
Frequency: 6, 6, 12, 11, 10, 5
(a) Draw the cumulative frequency graph of the data.
(b) From your graph, estimate the: (i) median; (ii) 80th percentile
(c) What is the modal weekly profit?
Show the model answer
(a) Upper class boundaries 10.5, 20.5, 30.5, 40.5, 50.5, 60.5 with cumulative frequencies 6, 12, 24, 35, 45, 50. Plot these (start at (0.5, 0)) and draw a smooth ogive.
(b)(i) Median at the 25th value: about N31 (calculation: 30.5 + (1/11) × 10 = 31.4)
(ii) 80th percentile at the 40th value: about N45.5 (40.5 + (5/10) × 10)
(c) The modal class is N21–N30 (frequency 12); estimated mode = 20.5 + 6/(6 + 1) × 10 ≈ N29
Plot cumulative frequency against the upper class boundary, not the class mark.