Question

A group of 360 people was asked to vote for their favorite season from the three seasons rainy, winter, and summer.
i) Which season got the most votes?
ii) Find the central angle of each sector.
iii) Draw a pie chart to show this information.

Season	No. of votes
Summer	90
Rainy	120
Winter	150

Answer 1

Hint: For part (i), find the season who got the maximum number of votes from the table. For part (ii), find the total number of votes. Then divide each season vote by total votes and multiply it by ${360}^{\circ }$ to get the central angle of each sector. For part (iii), draw a circle and use a protractor to draw the angles of each season.

Complete Step by Step Solution:
(i)
Since the number of votes for winter is 150 which is highest among all three seasons.
Hence, winter got the most votes.
(ii)
To calculate the total number of votes, add votes of all the seasons,
$\Rightarrow$Total vote $=90+120+150$
Add the terms on the right side,
$\therefore$ Total vote = $360$
Divide votes of each season vote with 360 and multiply it by 360.
For the summer season,
$\Rightarrow$ Central Angle $={\displaystyle \frac{90}{360}}\times {360}^{\circ }$
Cancel out the common term,
$\Rightarrow$ Central Angle $={90}^{\circ }$
For the rainy season,
$\Rightarrow$ Central Angle $={\displaystyle \frac{120}{360}}\times {360}^{\circ }$
Cancel out the common term,
$\Rightarrow$ Central Angle $={120}^{\circ }$
For the winter season,
$\Rightarrow$ Central Angle $={\displaystyle \frac{150}{360}}\times {360}^{\circ }$
Cancel out the common term,
$\Rightarrow$ Central Angle $={150}^{\circ }$
Hence, the central angle for summer is ${90}^{\circ }$, for rainy is ${120}^{\circ }$ and for winter is ${150}^{\circ }$.
(iii)
Draw a circle with a certain radius and mark its center.
Draw a radius at any point on the circle and using this radius of the circle as the base of the protractor, marks ${150}^{\circ }$ which is the highest angle on it, and name it.

Using the radius, mark the next highest angle, and name them.

Note: A pie-chart is a representation of data in a circle that is divided into several sections. Each division in the circle represents a proportion of the whole data. In general, every division of the circle is highlighted in a particular color and has a percentage and item heading labeled for it.