Pie Chart



In a pie chart, the various observations or components are represented by the sectors of a circle and the whole circle represents the sum of the values of all components.


The central angle for a component is given by:

Central angle for a component = \(\frac{\textbf{Value of the component}}{\textbf{Sum of the values of all components}}\) × 360°



How to make a pie chart or graph? 

Construction of making a pie chart or graph from the given data. 

Steps of pie graphs Construction:

1. Calculate the central angle for each component, given by 

Central angle of component = \(\frac{\textbf{Value of the component}}{\textbf{Total value}}\) × 360°



2. Draw a circle of convenient radius.

3. Within this circle, draw a horizontal radius.

4. Starting with the horizontal radius, draw radii making central angles corresponding to the values of the respective components, till all the components are exhausted. These radii divide the whole circle into various sectors.

5. Shade each sector with different design.

This will be the required pie chart for the given data.


Pie chart examples on how to do a pie chart:

1. Mr. Bin's with a yearly salary of $ 10800 plans his budget for a year as given below:

   Item     Food   Education   Rent   Savings  Miscellaneous
Amount (in dollar)
3150
1950
2100
2400
1200

Represent the above data by a pie graph.

Solution:

Total amount earned by Mr. Bin in a year = $ 10800.

Central angle of component = \(\frac{\textbf{Value of the component}}{\textbf{Total value}}\) × 360°

Calculation of central angles

   Item    Amount (in $)   Central Angle 
Food
3150
(³¹⁵/₁₀₈₀₀ × 360)° = 105°
Education
1950
(¹⁹⁵/₁₀₈₀₀ × 360)° = 65°
Rent
2100
(²¹/₁₀₈₀₀ × 360)° = 70°
Savings
2400
(²⁴/₁₀₈₀₀ × 360)° = 80°
Miscellaneous
1200
(¹²/₁₀₈₀₀ × 360)° = 40°


Construction of making pie chart

Steps of construction:

1. Draw a circle of any convenient radius.

2. Draw a horizontal radius of this circle.

3. Draw sectors starting from the horizontal radious with central angles of 105 degree, 65 degree, 70 degree, 80 degree and 40 degree respectively.

4. Shade the sectors differently using different colors and label them.

Thus, we obtain the required pie chart, as shown in the given figure.


2. The data on the mode of transport used by 720 students are given below:

   Mode of Transport      Bus     Cycle    Train    Car     Scooter  
No. of Students
120
180
240
80
100

Represent the above data by a pie chart.

Solution:

Total number of students = 720.

Central angle for a mode of transport = \(\frac{\textbf{Number of students using that mode}}{\textbf{Total number of students}}\) × 360°


Calculation of central angles

    Mode of Transport      No. of Students     Central Angle 
Bus
120
(¹²/₇₂₀ × 360)° = 60°
Cycle
180
(¹⁸/₇₂₀ × 360)° = 90°
Train
240
(²⁴/₇₂₀ × 360)° = 120°
Car
80
(/₇₂₀ × 360)° = 40°
Scooter
100
(¹/₇₂₀ × 360)° = 50°


Construction for creating pie chart

Steps of construction:

1. Draw a circle of any convenient radius.

2. Draw a horizontal radius of this circle.

3. Draw sectors starting from the horizontal radious with central angles of 60 degree, 90 degree, 120 degree , 40 degree and 50 degree respectively.

4. Shade the sectors differently using different colors and label them.

Thus, we obtain the required pie chart, as shown in the given figure.



3. There are 216 workers in a factory as per list given below: 

   Cadre     Labourer    Mechanic    Fitter    Supervisor    Clerk  
No. of Workers
75
60
36
27
18

Represent the above data by a pie chart.

Solution:

Total number of workers = 216.

Central angle for a cadre = \(\frac{\textbf{Number of workers in that cadre}}{\textbf{Total number of workers}}\) × 360°


Calculation of central angles

    Cadre      No. of Workers     Central Angle 
Labourer
75
(⁷⁵/₂₁₆ × 360)° = 125°
Mechanic
60
(/₂₁₆ × 360)° = 100°
Fitter
36
(³⁶/₂₁₆ × 360)° = 60°
Supervisor
27
(²⁷/₂₁₆ × 360)° = 45°
Clerk
18
(¹⁸/₂₁₆ × 360)° = 30°


Construction to make a pie graph

Steps of construction:

1. Draw a circle of any convenient radius.

2. Draw a horizontal radius of this circle.

3. Draw sectors starting from the horizontal radious with central angles of 125 degree, 100 degree, 60 degree, 45 degree and 30 degree respectively.

4. Shade the sectors differently using different colors and label them.

Thus, we obtain the required pie chart, as shown in the given figure.


4. The following table shows the expenditure in percentage incurred on the construction of a house in a city:

   Item    Brick    Cement   Steel   Labour    Miscellaneous 
Expenditure
(in percentage)
15%
20%
10%
25%
30%

Represent the above data by a pie chart.

Solution:

Total percentage = 100.

Central angle for a component = \(\frac{\textbf{Value of the component}}{\textbf{100}}\) × 360°


Calculation of central angles

    Item      Expenditure (in percentage)    Central Angle 
Brick
15%
(¹⁵/₁₀₀ × 360)° = 54°
Cement
20%
(²/₁₀₀ × 360)° = 72°
Steel
10%
(¹/₁₀₀ × 360)° = 36°
Labour
25%
(²⁵/₁₀₀ × 360)° = 90°
Miscellaneous
30%
(³/₁₀₀ × 360)° = 108°


Construction for creating pie chart

Steps of construction:

1. Draw a circle of any convenient radius.

2. Draw a horizontal radius of the circle.

3. Draw sectors starting from the horizontal radious with central angles of 54 degree, 72 degree, 36 degree, 90 degree and 108 degree respectively.

4. Shade the sectors differently using different colors and label them.

Thus, we obtain the required pie chart, shown in the adjoining figure.


 Pie Charts or Pie Graphs

Pie Chart


 Pie Charts or Pie Graphs - Worksheets

Worksheet on Pie Chart









8th Grade Math Practice

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