Pie Chart

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:

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:

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:

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

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

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