Question

Given below is the result of an annual examination of a class, showing the percentage of students in each category.

First division	Second division	Third division	Failed
25%	45%	20%	10%

Represent the above data by a pie chart.

Answer 1

$$\begin{gathered} \mathrm{Total}\mathrm{percentage}=100 \\ \mathrm{Central}\mathrm{angle}\mathrm{of}\mathrm{each}\mathrm{category}=\left(\frac{\mathrm{value}\left(\mathrm{in}\%\right)\mathrm{of}\mathrm{each}\mathrm{category}}{100}\times 360\right)° \\ \mathbf{Calculation}\mathbf{}\mathbf{of}\mathbf{}\mathbf{central}\mathbf{}\mathbf{angles} \end{gathered}$$

Category	Result (in %)	Central angle
First division	25	$90°$
Second division	45	$162°$
Third division	20	$72°$
Failed	10	$36°$

$$\begin{gathered} \mathbf{Construction}\mathbf{}\mathbf{of}\mathbf{}\mathbf{pie}\mathbf{}\mathbf{chart} \\ \mathrm{Steps}\mathrm{of}\mathrm{construction}: \\ 1.\mathrm{Draw}\mathrm{a}\mathrm{circle}\mathrm{of}\mathrm{any}\mathrm{convenient}\mathrm{radius}. \\ 2.\mathrm{Draw}\mathrm{a}\mathrm{horizontal}\mathrm{radius}\mathrm{of}\mathrm{the}\mathrm{circle}. \\ 3.\mathrm{Starting}\mathrm{from}\mathrm{the}\mathrm{horizontal}\mathrm{radius},\mathrm{draw}\mathrm{sectors}\mathrm{whose}\mathrm{central}\mathrm{angles}\mathrm{are}90°,162°,72°\mathrm{and}36°. \\ 4.\mathrm{Shade}\mathrm{the}\mathrm{sectors}\mathrm{so}\mathrm{obtained}\mathrm{differently}\mathrm{and}\mathrm{label}\mathrm{each}\mathrm{one}\mathrm{of}\mathrm{them}. \\ \mathrm{Thus},\mathrm{we}\mathrm{obtain}\mathrm{the}\mathrm{required}\mathrm{pie}\mathrm{chart}\mathrm{as}\mathrm{shown}\mathrm{in}\mathrm{the}\mathrm{figure}\mathrm{below}. \end{gathered}$$