question_answer 7)

                A group of 360 people were asked to vote for their favourite season from the three seasons rainy, winter and summer.

Season	No. of Votes
Summer	90
Rainy	120
Winter	150

(i) Which season got the most votes? (ii) Find the central angle of each sector. (iii) Draw a pie chart to show this information.

Answer:

                (i) Winter season got the most votes. (ii) Central angle of winter sector \[=\frac{\begin{align}   & \text{Number of people who vote} \\  & \text{                        for}\,\text{winter}\,\text{season} \\ \end{align}}{\text{Total}\,\text{number}\,\text{of}\,\text{people}}\,\ \times {{360}^{\text{o}}}\] \[=\frac{150}{360}\times 360{{}^{\text{o}}}\times {{150}^{\text{o}}}\] Central angle of summer sector \[\text{=}\frac{\begin{align}   & \text{Number of people who vote} \\  & \text{                 }\,\,\,\,\,\,\,\,\,\,\,\text{for}\,\text{summer}\,\text{season} \\ \end{align}}{\text{Total}\,\text{number}\,\text{of}\,\text{people}}\,\ \text{ }\!\!\times\!\!\text{ 36}{{\text{0}}^{\text{o}}}\] \[=\frac{90}{360}\times {{360}^{\text{o}}}={{90}^{\text{o}}}\] Central angle of rainy sector \[\text{=}\frac{\begin{align}   & \text{Number of people who vote } \\  & \,\,\,\,\,\,\,\,\,\,\text{                        for}\,\text{rainy}\,\text{season} \\ \end{align}}{\text{Total}\,\text{number}\,\text{of}\,\text{people}}\,\ \text{ }\!\!\times\!\!\text{ 36}{{\text{0}}^{\text{o}}}\] \[=\frac{120}{360}\times {{360}^{\text{o}}}={{120}^{\text{o}}}\]                 (iii)

Season	People who Voted for it	In fraction	Central angle
Winter	150	\[\frac{5}{12}\]	\[\frac{5}{12}\] of \[{{360}^{\text{o}}}={{150}^{\text{o}}}\]
Summer	90	\[\frac{1}{4}\]	\[\frac{1}{4}\] of \[{{360}^{\text{o}}}={{90}^{\text{o}}}\]
Rainy	120	\[\frac{1}{3}\]	\[\frac{1}{3}\] of \[{{360}^{\text{o}}}={{120}^{\text{o}}}\]

Pie chart