# Pie Charts Examples, Questions and Solutions

Pie charts are a typical type of data representation where data is represented as a part of a circle. The circle represents the total value (or 100%), and the different parts represent certain proportions (or percentage) of the total. In a pie chart, the are length of each sector (and in turn its central angle and area), is proportional to the part it represents.
The origin of the pie chart is traced back to Florence Nightingale in 1858. This was the year when she presented a paper on the causes of deaths in her army in the eastern part of the world.
Following is the pie chart originally developed by Florence Nightingale in the year 1858. (Actually called by her as the ‘Polar Area Diagram’.)

The below graphic gives the number of deaths that occurred from the diseases that could have been prevented (in light grey), those that were the results of wounds (in dark, grey) and those due to other causes (in black).

### There are two approaches to constructing a pie chart from any given data.

A) Degree Approach: The central angle in a circle represents $360^{\circ}$ , so any part or segment in pie chart is calculated as a proportion of $360^{\circ}$.
B) Percentage Approach: In this case, any part or segment in a pie chart is calculated as a part of 100%.

If we convert the same pie chart into the degree format, we will be required to do the following conversions:

 Total = 100 = $360^{\circ}$ Hence = 1% = $3.6^{\circ}$ Center = 10% = $36^{\circ}$ North = 20% = $72^{\circ}$ South = 25% = $90^{\circ}$ East = 15% = $54^{\circ}$ West = 30% = $108^{\circ}$

## Limitations of Pie Charts

Despite the pie chart being one of the most important ways to represent data, it is marred by limitations of its own:

• Pie charts can be used only when the sum of all categories is given, for example if the categories represent proportions or percentage of a total.
• A single pie chart can represent only one continuous variable.

Prerequisites (Related Formulas)
In pie charts, from geometry, we know that the area the sector of a circle must be proportional to the corresponding value of the component.
Since the sum of all the central angle is 360°, we have
Central angle of the component = {(value of the component/Total value) x 360} °.

## Significance of Pie Charts

The pie chart has gained prominence due to the following reasons:

• In a pie chart, we get a clear picture of the contribution of different sectors to the buildup of the total. E.g.., presentation of budgets.
• Comparing two pie charts is easier than comparing two bar charts or any other format of data representation.

Let us see the following data :

Sale value in 2005 = Rs 180 crores
Sale value in 2006 = Rs 204 crores

Example 1: What is the presentation increase in the sales value of the East zone?

Solution: There are two percentage increase (A) Total total sales value of company XYZ is increasing. (B) The percentage contribution of the East zone is increasing.
Percentage increase in The total sales value of the company XYZ = 30%
Percentage increase in the percentage contribution of the East zone = 20%
Hence, the net percentage increase = 56%
(Successive increase of 20% and 30%)

## Type of Pie Charts

There are two of pie charts :
(A) Normal Pie Chart
This displays the contribution of each component of the pic.

(B) Exploded Pie Chart

This pie chart has all the characteristics of a normal pie chart, the only addition is that the contribution of individual segments is highlighted.

## Solve Examples for Pie Chats

Example 1: The following pie-charts show the distribution of students of graduate and post-graduate levels in seven different institutes in a town. [Bank P.O. 2003]

1. What is the total number of graduate and post-graduate level students is institute R?

A. 8320
B. 7916
C. 9116
D. 8099

Required number = (17% of 27300) + (14% of 24700)
= 4641 + 3458
= 8099.

2. What is the ratio between the number of students studying at post-graduate and graduate levels respectively from institute S?

A. 14:19
B. 19:21
C. 17:21
D. 19:14

Required ratio = $\frac{21\ % of 24700}{14\ % of 27300} = \frac{(21\times 24700)}{14\times 27300} = \frac{19}{14}$

3. How many students of institutes of M and S are studying at graduate level?

A. 7516
B. 8463
C. 9127
D. 9404

Students of institute M at graduate level= 17% of 27300 = 4641.
Students of institute S at graduate level = 14% of 27300 = 3822.
$\therefore$ Total number of students at graduate in institutes M and S

Example 2: The following pie charts exhibit the distribution of the overseas tourist traffic from India. The two charts show the tourist distribution by country and the age profiles of the tourists respectively. [NABARD, 2001]

1. What percentage of Indian tourist went to either USA or UK?

A.40 %
B.50 %
C.60 %
D.70 %

(40+10) = 50% (from first chart)

2. The ratio of the number of Indian tourists that went to USA to the number of Indian tourists who were below 30 years of age is ?
A.2:1
B.8:3
C.3:8
D. cannot be determined

40:15 = 8:3

3. If amongst other countries, Switzerland accounted for 25% of the Indian tourist traffic, and it is known from official Swiss records that a total of 25 lakh Indian tourists had gone to Switzerland during the year, then find the number of 30-39 year old Indian tourists who went abroad in that year ?

A. Rs.18.75 lakh
B. Rs. 25 lakh
C. Rs. 50 lakh
D. Rs. 75 lakh

Tourist traffic from other countries to Swiz is 20%.
Amongst this 20%, 25% of traffic from India.
So, 25% of 20% = 5% corresponds to the Indian traffic in Switzerland.
5 % corresponds to Switzerland's 25 lakh. Hence 15% will be 75 lakh.

Directions for questions 1to 5 : Refer to the following pie chart and solve the questions based on it.
Following is the cost analysis of a book “Pearson’s Guide to Quantitative Aptitude for CAT”.

4. What is the central angle showing the cost of paper?

Answer : $57.6^{\circ}$
Required Angle = $(\frac{16}{100}\times 360)$ = $57.6^{\circ}$

5. If the cost of printing is Rs. 23,400 what would the cost of royalty be?

6. If the miscellaneous expenditure amounts to Rs. 18,000 then what is the expenditure on editing?

7. The royalty on the book is less than the editing expenditure by
If the editing charges are Rs 18, royalty is Rs 10. On Rs 18, it is less by 8. On Rs 100, it is less by$(\frac{8}{18}\times 100)$% = 44.44%

8. If 5500 copies of the book are published and the miscellaneous expenditure amounts to Rs. 36,960 and the marked price is 40% above the cost price, then the marked price of each copy is
Let the total expenditure ‘be Rs x. Then, 8 : 100 = 36960 : x. So x = Rs 462000. Therefore Cost Price of 5500 copies of the book = Rs 4,62,000. Cost Price of each copy = Rs $(\frac{42,62,000}{500})$ = Rs 84. So, marked price = 140% of Rs 84 = Rs 117.60.

## Pie Chart Questions from Previous Year Exams

This test will cover Pie-Chart syllabus of Bank Clerk Exam.

## Pie Chart - Video Tutorials

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