Question

10. The table below shows the frequency distribution of the marks scored by 200 candidates in an examination. Marks (%): 0-9,10-19,20-29,30-39,40-49,50-59,60-69,70-79,80-89,90-99 | Frequency: 7,11,17,20,29,34,30,25,21,6. (a) Construct a cumulative frequency table for the data. (b) Draw a cumulative frequency curve (ogive) for the data. (c) Using your graph, estimate: (i) Median score; (ii) Lowest mark for distinction, if 5% of the candidates made the distinction.

Accepted Answer

(a) Cumulative frequency table (Upper Class Boundary, Frequency, Cumulative Frequency): 9.5,7,7 | 19.5,11,18 | 29.5,17,35 | 39.5,20,55 | 49.5,29,84 | 59.5,34,118 | 69.5,30,148 | 79.5,25,173 | 89.5,21,194 | 99.5,6,200.
(b) [Ogive plotted: cumulative frequency (y-axis, 0-200) against upper class boundary (x-axis, 0-100), forming a smooth S-shaped curve rising from (9.5,7) to (99.5,200).]
(c)(i) For the median, N/2 = 200/2 = 100th mark. Tracing from the ogive at cumulative frequency 100, the median score corresponds to approximately 54.25%.
(ii) If 5% of the candidates made the distinction, this corresponds to the top 5%, i.e. the (100-5)% = 95th percentile, equivalent to (95/100) x 200 = 190th mark. Tracing from the ogive at cumulative frequency 190 gives the lowest mark for distinction as approximately 87.6%.

WAEC Mathematics 2020 Theory — Question 10

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