# 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 (⁸/₇₂₀ × 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 (⁶/₂₁₆ × 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