Question

The following table shows the breakdown of a company's expenditure under different categorieses.

Type of expenditure	Machines	Electricity	Salary	Rent
Amount ($)	2000	2500	5000	500

Represent the above data by a pie chart.

• A.
• B.
• C.
• D. none of the above

Answer 1

The correct option is B

Type of expenditure	Machines	Electricity	Salary	Rent
Amount ($)	2000	2500	5000	500

Pie chart is a circular graph which is used to represent data. In this :

$\to$ The various data observations are represented by the circle's sectors.

$\to$ The whole circle represents the sum of the values of all the observations.

Hence, the sum of expenditures
= 2000 + 2500 + 5000 + 500 = 10000

$\to$ The total angle formed at the centre of a circle is 360°.

$\to$ The angle at the centre corresponding to the particular observation component is given by

$\text{Centre angle at a particular observation}=\frac{\text{Value of the particular observation}}{\text{Total value}}$

Hence, the centre angle corresponding to particular observation/component is evaluated as follows,

$\text{Central angle of the machines sector}=\frac{\text{Amount spend on machines}}{\text{Total expenditures}}\times {360}^{\circ }$
$=\frac{2000}{10000}\times {360}^{\circ }$
$=\frac{1}{5}\times {360}^{\circ }$
$={72}^{\circ }$

$\text{Central angle of the electricity sector}=\frac{\text{Amount spend on electricity}}{\text{Total expenditures}}\times {360}^{\circ }$
$=\frac{2500}{10000}\times {360}^{\circ }$
$=\frac{1}{4}\times {360}^{\circ }$
$={90}^{\circ }$

$\text{Central angle of the salary sector}=\frac{\text{Amount spend on salary}}{\text{Total expenditures}}\times {360}^{\circ }$
$=\frac{5000}{10000}\times {360}^{\circ }$
$=\frac{1}{2}\times {360}^{\circ }$
$={180}^{\circ }$

$\text{Central angle of the rent sector}=\frac{\text{Amount spend on rent}}{\text{Total expenditures}}\times {360}^{\circ }$
$=\frac{500}{10000}\times {360}^{\circ }$
$=\frac{1}{20}\times {360}^{\circ }$
$={18}^{\circ }$

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