## Pie chart

#### Data Interpretation Tutorial

A circular chart is also called a pie chart. In which , all information about various types of items or income, expenditure of any individual person(such as education, transport, food, clothes, rent, and others) is given in many sectors or parts, depending on the adequate information given to them, we are answered to different types of questions. In the questions of pie chart , the total quantity is distributed over a total angle of 360° or 100% .
In each chart, each part is proportional to the arc length , its central angle and area given amount , which its shows. The entire pie chart contains 360° angle in circular chart.it is used to make comparative study of given samples. The answers to the questions asked on the basis of these can be easily answered.

#### 1. When Data is given in form of percentage :-

In this type of pie chart , If data is given as a percentage , then the total value of all its parts is 100%.

 Actual value of any part = Percentage value of that part x Total actual value 100

 And Percentage value of that part = Actual value of any part x 100% Total actual value

Example 1. Directions : The pie-chart drawn below shows the expenses of a family on various items and its savings during the year 2001. Study the graph and answer the questions given below:

(i) Maximum expenditure of the family was on
Sol :- From above given graph ,
According to given option in question , Maximum expenditure of the family is on food ,which is 23%.

(ii) The total savings of the family for the year were equal to the expenditure on:
Sol :- From above given graph ,
The total savings of the family for 2001 year will be equal to the expenditure on housing , which is 15%.
i.e. Expenditure on housing = Savings = 15%.

(iii) What percent of the income was spent on transport and other items together?
Sol :- From above given graph ,
Expenditure on transport and other items = (20 + 5) % = 25%.
total income = 100%

(iv) If the total income of the family was \$ 100000, how much money was spent on the education of children?
Sol :- Given , Total income of the family = \$ 100000
From above given graph ,
Expenditure on the education of the children = 12% of \$ 100000

 ∴ Expenditure on the education of the children = 12 x 100000 = \$ 12000 100

(v) If the total income for the year was \$ 100000, the difference of the expenses between housing and transport was:
Sol :- Given , total income = \$ 100000
From above given graph ,
The percentage difference in expenditure on housing and transport = (15 – 5) % = 10%
The required difference = The percentage difference in expenditure on housing and transport x \$ 100000
The required difference = 10% of \$ 100000

 The required difference = 10 x 100000 = \$ 10000 100

#### 2. When Data is given in form of Degree :-

In this type of pie chart , If data is given as a degree , then the total value of all its parts is 360°.

 Actual value of any part = Degree value of that part x Total actual value 360°

And

 Degree value of that part = Actual value of any part x 360° Total actual value

Example 2. Directions : The annual agricultural production (in tonnes) of an Indian state is given in the pie chart. The total production is 9000 tonnes. Read the pie chart and answer the question.

(i) What is the annual production of wheat?

Sol :- Given that , 360° = 9000 tonnes

 1° = 9000 = 25 360

∴ 110° = 25 x 110 = 2750 tonnes

Example 3. Direction : The pie chart given below represents the number of students using different transport to a school in which total number of students is 2160. Answer the questions based on the following diagram.

(i) The total number of students who come to school by car is:
Sol :- From above the given pie chart ,

 The total number of students who come to school by car = 70° x 2160 = 7 x 60 = 420 360°

(ii) The ratio of the total number of students who come to school by car to the total number of students who come to school by bus is:
Sol :- From above the given pie chart ,

 Total number of students who come to school by car = 70° = 70° = 90° x 2160 = 420 360°

 Total number of students who come to school by bus = 90° = 90° x 2160 = 540 360°

Required ratio = Total number of students who come to school by car : Total number of students who come to school by bus = 420 : 540 = 21 : 27

(iii) The total number of students coming to school either by walking or by bus is:
Sol :- As per the given pie chart ,
Total number of students = 2160

 = ( Total number of students who come to school by walking + Total number of students who come to school by bus ) x total number of students 360°

 Required answer = ( 80° + 90° ) x 2160 = 1020 360°

(iv) The total number of students who don’t come to school by train is:
Sol :- From the above given pie chart ,
Total number of students = 2160
Total number of students who come to school by train = 120°

 Required answer = ( 360° - 120° ) x 2160 = 1440 360°

(v) The total number of students coming to school by bus exceeds the total number of students coming to school by walking, by:
Sol :- From the above given pie chart ,
Total number of students coming to school by bus = 90°
Total number of students coming to school by walking = 80°
Total change = Total number of students coming to school by bus - Total number of students coming to school by walking = 90° - 80° = 10°

 ∴ Required percent = Total change x 100% Total number of students coming to school by walking

 Required answer = 10 x 100% = 12.5% 80

#### 3. When Data is given in form of Actual value :-

In this type of pie chart , If data is given as actual value , then these type of problems we can easily solve it .

#### Relation between percentage and degree :-

We know that The total value of all the given sectors or parts in any pie chart is 100% or 360 & deg; .

100% ≡ 360°