Question

Draw a pie chart showing the following information. The table shows the colors preferred by a group of people.

Colors	Number of People
Blue	18
Red	9
Green	6
Violet	3
Total	36

Find the proportion of each sector. For eg.,
Blue is $\dfrac{18}{36}=\dfrac{1}{2}$ ; Red is $\dfrac{9}{36}=\dfrac{1}{4}$ and so on. Use this to find the corresponding angles.

Answer 1

Hint: First of all, we are going to find the proportion of people in each color which we will do by dividing the given number of people to the total number of people. After getting the proportion of each color, we are going to multiply each proportion to the angle ${{360}^{\circ }}$ to get the share of angle corresponding to that color. And hence, we will draw the pie chart.

Complete step by step answer:
The table given in the above problem through which we have to construct a pie chart is as follows:

Colors	Number of People
Blue	18
Red	9
Green	6
Violet	3
Total	36

Now, to draw the pie chart corresponding to the number of different sets of people which have opted different colors we are going to first of all find the proportion of people in each color type.
Proportion of people opted blue color is calculated by dividing 18 to 36 we get,
$\begin{align}
  & \dfrac{18}{36} \\
 & =\dfrac{1}{2} \\
\end{align}$
Proportion of people who have opted red color is calculated by dividing 9 to 36 we get,
$\begin{align}
  & \dfrac{9}{36} \\
 & =\dfrac{1}{4} \\
\end{align}$
Proportion of people who have opted green color is calculated by dividing 6 to 36 we get,
$\begin{align}
  & \dfrac{6}{36} \\
 & =\dfrac{1}{6} \\
\end{align}$
Proportion of people who have opted violet color is calculated by dividing 3 to 36 we get,
$\begin{align}
  & \dfrac{3}{36} \\
 & =\dfrac{1}{12} \\
\end{align}$
Now, to draw a pie chart, we should know the angle of the sector corresponding to different sets of people who have opted different colors.
Angle we are going to calculate by multiplying each proportion that we have calculated above to ${{360}^{\circ }}$.
Hence, in the pie chart, the colors blue, red, green and violet possess these many angles respectively.
Angle of sector corresponding to blue color is equal to:
$\begin{align}
  & \dfrac{1}{2}\times {{360}^{\circ }} \\
 & ={{180}^{\circ }} \\
\end{align}$
Angle of sector corresponding to red color is equal to:
$\begin{align}
  & \dfrac{1}{4}\times {{360}^{\circ }} \\
 & ={{90}^{\circ }} \\
\end{align}$
Angle of sector corresponding to green color is equal to:
$\begin{align}
  & \dfrac{1}{6}\times {{360}^{\circ }} \\
 & ={{60}^{\circ }} \\
\end{align}$
Angle of sector corresponding to violet color is equal to:
$\begin{align}
  & \dfrac{1}{12}\times {{360}^{\circ }} \\
 & ={{30}^{\circ }} \\
\end{align}$
Now, according to angle distribution of the colors we are going to draw a pie chart as follows:

In the above diagram, we have written the number of people who have opted for that particular color. As you can see, in the blue color area, number 18 is written which is showing that 18 people opted blue color. Similarly, you can see red, green and violet colors also.
Hence, we have drawn the pie chart.

Note: In the above solution, you might be thinking that why we have multiplied the proportion corresponding to each color by ${{360}^{\circ }}$. The answer is, the whole pie, is of ${{360}^{\circ }}$ which you can consider as a circle and we know that central angle of the circle is ${{360}^{\circ }}$.
The mistake that could happen is the calculation mistakes so make sure you won’t mess up with the calculations.