Question

Represent the following data by a pie diagram:

Items of expenditure	Expenditure
	Family A	Family B
Food	4000	6400
Clothing	2500	480
Rent	1500	3200
Education	400	1000
Miscellaneous	1600	600
Total	10000	11680

Answer 1

Hint: In this question, we are given data on expenditure for two families and we have to draw a pie chart for both of them. For this, we will first change the expenditure of different items into central angles (degrees) for a circle using the formula:
\[\text{Central angle of component}=\dfrac{\text{Component Value}}{\text{Sum of all components}}\times 360\]
After that, we will make a pie chart using these degrees for both families.

Complete step-by-step solution:
Let us first change the expenditure for different items of both families into central angles. We will do it using the formula:
\[\text{Central angle of component}=\dfrac{\text{Component Value}}{\text{Sum of all components}}\times 360\]
Let us draw a table for both families and find degrees in the table.
Here, the sum of all components is 10000 for family A and 11680 for family B.

Items of expenditure	Family A	Family B
	Expenditure	Sector angle	Expenditure	Sector angle
Food	4000	$\dfrac{4000}{10000}\times 360=144$	6400	$\dfrac{6400}{11680}\times 360=197.3$
Clothing	2500	$\dfrac{2500}{10000}\times 360=90$	480	$\dfrac{480}{11680}\times 360=14.8$
Rent	1500	$\dfrac{1500}{10000}\times 360=54$	3200	$\dfrac{3200}{11680}\times 360=98.6$
Education	400	$\dfrac{1600}{10000}\times 360=57.6$	1000	$\dfrac{600}{11680}\times 360=18.5$
Miscellaneous	1600	$\dfrac{400}{10000}\times 360=14.4$	600	$\dfrac{1000}{11680}\times 360=30.8$

Now, let us understand the steps involved in making pie charts.
Step 1: Draw a 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 for family A is ${{144}^{\circ }}$. So, for family, A draw a sector with central angle ${{144}^{\circ }}$ in such a way that one of its radii coincide with the radius drawn in step 2 and another radius is in its counter-clockwise direction. Similarly, family B starts with ${{197.3}^{\circ }}$.
Step 4: Construct other sectors representing other items in the clockwise sense in descending order of magnitude of their central angles.
Step 5: Shade the sectors with different patterns and label them.
Now, let us draw pie charts for both families using the above steps.

Note: Students should carefully convert given data into central angles (degrees) to make pie charts. While drawing the last sector the radius should coincide with the first drawn radius. Make sure that the sum of all degrees becomes equal to ${{360}^{\circ }}$.