The pie chart shows the distribution of marks... | WAEC SSCE - General Mathematics - 2000 (Essay)

Question 1 Report

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 marks ?

(b) What fraction of the pupils scored at most 50 marks?

Answer

Reading the pie chart. The whole circle (\(360^\circ\)) represents all \(200\) pupils, so each degree stands for \(\frac{200}{360}=\frac{5}{9}\) of a pupil. The sectors read off the diagram are:

Class (marks)	Angle
31 - 40	\(54^\circ\)
41 - 50	\(90^\circ\)
51 - 60	\(108^\circ\)
61 - 70	\(54^\circ\)
71 - 80	\(36^\circ\)
81 - 90	\(18^\circ\)

Check: \(54+90+108+54+36+18=360^\circ\). Good.

(a)(i) Pupils scoring between 41 and 50. This is the \(90^\circ\) sector.

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

(a)(ii) Pupils scoring above 80. This is the \(81\text{-}90\) sector, \(18^\circ\).

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

(b) Fraction scoring at most 50 marks. “At most 50” means the \(31\text{-}40\) and \(41\text{-}50\) classes together: \(54^\circ+90^\circ=144^\circ\).

\[\text{Fraction}=\frac{144}{360}=\frac{2}{5}.\]

(c) Modal class. The modal class is the one with the greatest sector angle (largest frequency), which is \(108^\circ\).

Therefore the modal class is 51 - 60.

Read lesson note on Mensuration (JAMB)

Answer Details