Question

11. The frequency distribution table shows the marks obtained by 100 students in a Mathematics test.
Marks(%): 1-10, 11-20, 21-30, 31-40, 41-50, 51-60, 61-70, 71-80, 81-90, 91-100
Frequency: 2, 3, 5, 13, 19, 31, 13, 9, 4, 1
(a) Draw a cumulative frequency curve for the distribution.
(b) Use the graph to find the: (i) 60th percentile; (ii) probability that a student passed the test if the pass mark was fixed at 35%.

Accepted Answer

(a) Using class boundaries (0.5–10.5, 10.5–20.5, ..., 90.5–100.5) and their cumulative frequencies (2, 5, 10, 23, 42, 73, 86, 95, 99, 100), the cumulative frequency (ogive) curve is plotted with class upper boundaries on the x-axis and cumulative frequency (or cumulative %) on the y-axis, forming a smooth S-shaped (ogive) curve.

(b)(i) For the 60th percentile, 60% of 100 = 60. Tracing this value from the cumulative frequency (%) axis to the curve and then down to the marks axis gives approximately 56.5 as the 60th percentile.
(ii) Tracing 35% marks on the x-axis up to the curve and across gives approximately 14 on the y-axis, meaning that 14 out of 100 got less than 35%. Therefore, (100−14)=86 students got 35% and above. The required probability = 86/100 = 0.86.

WAEC Mathematics 2013 Theory — Question 12

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