Question

Given below is the result of an exam, showing the number of students in each category.

First division	Second division	Third division	Failed
20	100	50	30

Represent the above data by a pie chart.

• A.
• B.
• C.
• D. None of the above

Answer 1

The correct option is A

First Division	Second Division	Third Division	Failed
20	100	50	30

Total number of students $=20+100+50+30=200$

$\text{Central angle of the first division sector}=\frac{\text{Number of students in the first division}}{\text{Total number of students}}\times {360}^{\circ }$
$=\frac{20}{200}\times {360}^{\circ }$
$=\frac{1}{10}\times {360}^{\circ }$
$={36}^{\circ }$

$\text{Central angle of the second division sector}=\frac{\text{Number of students in the second division}}{\text{Total number of students}}\times {360}^{\circ }$
$=\frac{100}{200}\times {360}^{\circ }$
$=\frac{1}{2}\times {360}^{\circ }$
$={180}^{\circ }$

$\text{Central angle of the third division sector}=\frac{\text{Number of students in the third division}}{\text{Total number of students}}\times {360}^{\circ }$
$=\frac{50}{200}\times {360}^{\circ }$
$=\frac{1}{4}\times {360}^{\circ }$
$={90}^{\circ }$

$\text{Central angle of the failed sector}=\frac{\text{Number of students failed}}{\text{Total number of students}}\times {360}^{\circ }$
$=\frac{30}{200}\times {360}^{\circ }$
$=\frac{3}{20}\times 20\times {18}^{\circ }$
$=3\times {18}^{\circ }$
$={54}^{\circ }$

Hence, option (a.) is the correct choice.