# Data Interpretation Pie Chart

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Data interpretation of the pie chart is the representation of data in a circle that is divided into various sectors. These sectors are constructed in such a way that the area of each sector is proportional to the corresponding magnitude of the data represented by the sector.

## Some useful points in data interpretation of pie chart:

• Here, different sectors in a pie chart are considered as component parts.
• In a pie chart component parts are expressed in 3 types.
1. Either component values in percentages.
2. The fractional ratio of respective total value given.
3. Sector angle of respective total value given
• Since the pie chart is a circle and it has 360 degrees at its center which are equal to 100% of component values when added.
• 100% of component values represented on the pie chart are equal to 360 degrees angle of the pie chart.
100%=360 degrees
1%=3.6 degrees

So, when the percentage of component values is given they can be converted to a degree by multiplying each of the percentage values with 3.6 degrees.

## The formula for the angle of a sector:

But when component/sector value is not given in percentage then component/sector values can be represented by using the below the angle of sector formula.

Example problem:

Below pie chart shows the percentage of the number of students enrolled in a school / in different activities.

To convert the pie chart into degrees we need to do the following conversions:

 Total Percentage Degree Red cross 10 36 NCC 5 18 Human resource development club 10 36 Debating club 25 90 Eco club 20 72 Scout 30 108

#### Formula to find the percentage of a sector when the angle of the sector is given

Example problem:
Let us consider the Red Cross-sector from the above example

Percentage of Red Cross Sector=10
Total value is (Total Angle)=360 degrees
Therefore, the angle of the Red Cross sector=(10/100) ×360=36 degrees

#### Formulas to find the angle of a sector when the percentage of the sector is given

Example problem:
For this Red Cross-sector only let us consider the resultant angle 36 degrees and find percentage.

Here,
The angle of Red Cross sector=360 degrees
Total value is (Total percentage value)=100%
Percentage of Red Cross sector=(36/360)  × 100=10%

### Data interpretation pie chart example question with the solution:

Study the following pie chart given here which represents a domestic expenditure of family in percentage and answer the following questions. Total months income of the family is 55,750 rupees

1. House rent per month is

12/100 × 55,750

1. The annual savings in the form of provident fund is

(13/100)  × (55750 ×12)

Annual PF savings=13% of (55750 ×12)

1. The total amount per month, the family spends on food & entertainment combined together is

(18%+9%) ×55750

⇒ 27/100 ×55750