Theory question 112
StatisticsThe table shows the distribution of marks scored by some candidates in an examination
Marks: 11 − 20, 21 − 30, 31 − 40, 41 − 50, 51 − 60, 61 − 70, 71 − 80, 81 − 90, 91 − 100
Number of candidates: 5, 39, 14, 40, 57, 25, 11, 8, 1
(a) Construct a cumulative frequency table for the distribution. (b) Draw a cumulative frequency curve for the distribution. (c) Use the curve to estimate the: (i) number of candidates who scored marks between 24 and 58; (ii) lowest mark for distinction, if 12% of the candidates passed with distinction.
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(a) Upper class boundaries 20.5, 30.5, …, 100.5; cumulative frequencies 5, 44, 58, 98, 155, 180, 191, 199, 200 (total 200).
(b) Plot cumulative frequency against upper boundary (start at (10.5, 0)) and join with a smooth S-shaped curve.
(c)(i) From the curve: about 19 scored up to 24 and about 141 up to 58, so about 122 candidates.
(ii) 12% of 200 = 24 candidates, i.e. cumulative frequency 176: reading across gives a mark of about 69.
Plot cumulative frequencies at the upper class boundaries.