Question

The following data shows the expenditure of a person on different items during a month. Represent the data by a pie-chart.

$\begin{array}{cccccc}\text{Items of expenditure}& \text{Rent}& \text{Education}& \text{Food}& \text{Clothing}& \text{Others}\\ \text{Amount (in Rs)}& 2700& 1800& 2400& 1500& 2400\end{array}$

Answer 1

We know that,

Central angle of a component $=\frac{\text{component value}}{\text{sum of component values}}\times {360}^{\circ }$

Here, total amount $=Rs.10800$

Thus, the central angle for each component can be calculated as follows:

$\begin{array}{ccc}\text{Item}& \text{Amount (in Rs)}& \text{Sector angle}\\ \text{Rent}& 2700& \frac{2700}{10800}\times {360}^{\circ }={90}^{\circ }\\ \text{Education}& 1800& \frac{1800}{10800}\times {360}^{\circ }={60}^{\circ }\\ \text{Food}& 2400& \frac{2400}{10800}\times {360}^{\circ }={80}^{\circ }\\ \text{Clothing}& 1500& \frac{1500}{10800}\times {360}^{\circ }={50}^{\circ }\\ \text{Others}& 2400& \frac{2400}{10800}\times {360}^{\circ }={80}^{\circ }\end{array}$

Now, the pie chat representing the given data can be constructed by following the steps below:

Step 1: Draw circle of an appropriate radius.

Step 2: Draw a vertical radius of the circle drawn in step 1.

Step 3: Choose the largest central angle. Here, the largest central angle is ${90}^{\circ }$

. Draw a sector with the central angle ${90}^{\circ }$.

in such a way that one radius coincides with the radius drawn in step 2 and another radius is in its counter clockwise direction.

Step 4: Construct other sectors representing other items in the clockwise direction in descending order of magnitudes of their central angles.

​Step 5: Shade the sectors with different colours and label them, as shown as in the figure below.​​