The pie chart shows the distribution of marks scored by 200 pupils in a test. (a) How many pupils scored : (i) between 41 and 50 marks? ; (ii) above 80 mark...

(a)

(i) Pupils who scored between 41 and 50 marks

The sector for 41 to 50 marks has angle \(90^\circ\).

\[\frac{90}{360}\times 200=50\]

Therefore, 50 pupils scored between 41 and 50 marks.

(ii) Pupils who scored above 80 marks

The sector for marks above 80 has angle \(18^\circ\).

\[\frac{18}{360}\times 200=10\]

Therefore, 10 pupils scored above 80 marks.

(b) The angles representing pupils who scored at most 50 marks are \(54^\circ\) and \(90^\circ\).

\[\text{Required fraction}=\frac{54+90}{360}=\frac{144}{360}=\frac{2}{5}\]

Thus, the fraction is \(\boxed{\frac{2}{5}}\).

(c) The modal class is \(\boxed{51\text{–}60\text{ marks}}\), since it has the largest sector in the pie chart.