##
**Pie
Chart**

A

**pie chart**is a circular graph in which the angles of the different sectors represent the corresponding frequencies of different data.************************************

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In

**pie chart**, a circle is divided into as many sector as there are variables in a frequency distribution. The area of each sector is proportional to the relative frequency of the class represented by the sector. We know from geometry that the area of any sector is proportional to the angle subtended at the centre by its arc. So we make angle at the centre proportional to the various relative frequencies.
We know that the angle at the centre of a circle is
360°. So in order to get the angles of the desired sectors, we divide 360° in
the proportion of the various relative frequencies.

####
__Central
angle and sector__**:**

__Central angle and sector__

Any angle which has its vertex at the centre of a
circle is called central angle of that circle. ∠AOB
is the central angle in the adjoining figure. The shaded region is the sector.
If the degree measure of central angle is 1, then the sector is 1/360 of the
interior of the circle. If the degree measure of central angle is 30, then the
sector is 30 × 1/360 = 1/12 of the interior of the circle. If the whole
interior represents 100%, then the sector represents 1/12 × 100%.

####
__Conversion of frequency into degree__**:**

__Conversion of frequency into degree__

Add all the
frequencies to get the total number of data. Then we use the following formula
to get the central angle of corresponding frequencies of each data:

Central angle
= (corresponding frequency of data / sum of frequencies) × 360°

####
__Constructing Pie chart__**:**

__Constructing Pie chart__

We should use
the following steps to construct a pie chart:

__Step 1__: Calculate the sum of the data.

__Step 2__: The sum of data is compared with 360°.

__Step 3__: The central angle of a data = data/sum of data × 360°.

__Step 4__: Draw a circle of convenient size. Then draw a radius as a starting line.

__Step 5__: Use a protractor to construct the angles at the centre corresponding to each data.

###
*Workout
Examples*

*Workout Examples*

**Example 1: The monthly expenditure of Ram’s family is given in the table below. Construct the corresponding pie chart of the data.**

Items |
Education |
Food |
Rent |
Clothing |
Other |

Amount |
8000 |
12000 |
5000 |
4000 |
7000 |

*Solution:*

*Here,*

*Total expenditure = 8000+12000+5000+4000+7000*

*= 36000*

*Now,*

*Central angle for Education = (8000/36000)×360° = 80°*

*Central angle for Food = (12000/36000)×360° = 120°*

*Central angle for Rent = (5000/36000)×360° = 50°*

*Central angle for Clothing = (4000/36000)×360° = 40°*

*Central angle for Other = (7000/36000)×360° = 70°*

*Pie chart,*

*Example 2: Binesh’s monthly expenditure is Rs 25200. The diagram given below is a pie chart showing his expenditure on different headings. Find how much was spent under each heading.*

*Solution:*

*Here,*

*Total monthly expenditure = Rs. 25200*

*We know,*

*Expense amount for each item = (Angle/360) × Total expenditure*

*So expenses in,*

*Education = (95/360) × 25200 = Rs. 6650*

*Food = (100/360) × 25200 = Rs. 7000*

*Rent = (60/360) × 25200 = Rs. 4200*

*Transportation = (83/360) × 25200 = Rs. 5810*

*Others = (22/360) × 25200 = Rs. 1540*

*∴*

*Expense amount in each item is given in the table.*

Items |
Education |
Food |
Rent |
Transp. |
Other |

Amount in Rs. |
8000 |
12000 |
5000 |
4000 |
7000 |

*You can comment your questions or problems regarding*

**pie chart**here.
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