(a)

Scores (x)	1	2	3	4	5	7	8	9	10	Total
No of pupils (f)	1	1	5	3	\(k^{2} + 1\)	6	2	3	4	\(k^{2} + 26\)
fx	1	2	15	12	\(5k^{2} + 5\)	42	16	27	40	\(5k^{2} + 160\)

\(\bar{x} = \frac{\sum fx}{\sum f}\)
\(6 = \frac{5k^{2} + 160}{k^{2} + 26}\)
\(6(k^{2} + 26) = 5k^{2} + 160\)
\(6k^{2} + 156 = 5k^{2} + 160\)
\(6k^{2} - 5k^{2} = 160 - 156\)
\(k^{2} = 4\)
\( k = \sqrt{4} = 2\)
\(\therefore k = 2\)
(ii) \(Median = \frac{5 + 7}{2}\)
= \(\frac{12}{2} = 6\)
(b)



(c) Probability of scoring less than 6 = \(\frac{15}{30} \)
= \(\frac{1}{2}\)