(a)

Marks(x)	No of students(f)	Class boundaries	Cum Freq\((\sum f)\)
0-9	50	-0.5 - 9.5	50
10-19	50	9.5 - 19.5	100
20-29	40	19.5 - 29.5	140
30-39	60	29.5 - 39.5	200
40-49	100	39.5 - 49.5	300
50-59	100	49.5 - 59.5	400
60-69	50	59.5 - 69.5	450
70-79	25	69.5 - 79.5	475
80-89	15	79.5 - 89.5	490
90-99	10	89.5 - 99.5	500

(c)(i) Position of lower quartile, \(Q_{1} = \frac{\sum f + 1}{4} = \frac{500 + 1}{4}\)
= \(\frac{501}{4} = 125.25th\) position.
\(\therefore Q_{1} = 26.0\)
Position of upper quartile, \(Q_{3} = 3(\frac{\sum f + 1}{4}) = 3(125.25) = 375.75th\) position.
\(\therefore Q_{3} = 56.3\)
Semi-interquartile range = \(\frac{Q_{3} - Q_{1}}{2} = \frac{56.3 - 26}{2}\)
= \(\frac{30.3}{2} = 15.15\)
(ii) If the pass mark is 37, then 190 students failed.
(iii) Those who scored between 0% and 20% = 100
Those who scored between 0% and 60% = 400
Those who scored between 20% and 60% = 400 - 100 = 300.
P(20% < x < 60%) = \(\frac{300}{500} = \frac{3}{5}\)