Theory question 111
Data PresentationThe table below shows the scores of 2000 candidates in an entrance examination into a private secondary school.
% Marks: 11-20, 21-30, 31-40, 41-50, 51-60, 61-70, 71-80, 81-90
No. of Pupils: 68, 184, 294, 402, 480, 310, 164, 98
(a) Prepare a cumulative frequency table and draw the cumulative frequency curve for the distribution.
(b) Use your curve to estimate the: (i) cut-off mark, if 300 candidates are to be offered admission. (ii) probability that a candidate picked at random scored at least 45%.
Show the model answer
(a) Upper class boundaries 20.5, 30.5, 40.5, 50.5, 60.5, 70.5, 80.5, 90.5 with cumulative frequencies 68, 252, 546, 948, 1428, 1738, 1902, 2000; plot and draw a smooth ogive
(b)(i) 300 admitted means 2000 − 300 = 1700 below the cut-off; reading at 1700 gives about 69%
(ii) About 710 candidates scored below 45%, so about 1290 scored at least 45%
Probability ≈ 1290/2000 ≈ 0.65
Plot cumulative frequency against upper class boundaries; the top 300 lie above the 1700th candidate.