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...
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?
(c) What is the modal class?
Answer Details
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.
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