Learning Objectives
- You will get an understanding of what are Pie Charts and a first-hand view of how data is presented through its organisation in the form of Pie charts.
- You will get an understanding of typical data which can be represented through Pie charts. Also, understand the concept of how the distribution of a whole is done in the form of Pie Charts.
- You will get a first hand feel of the typical question types that are asked on the basis of Pie charts.
- Practice exercise on Pie charts containing simulated examination questions
Introduction
Pie charts are specific types of data presentation where the data is represented in the form of a circle. In a pie chart, a circle is divided into various sections or segments such that each sector or segment represents a certain proportion or percentage of the total. In such a diagram, the total of all the given items is equated to 360 degrees and the degrees of angles, representing different items, are calculated proportionately. The entire diagram looks like a pie and its components resemble slices cut from a pie. The pie chart is used to show the break-up of one continuous variable into its component parts.
The types of pie charts
There are two approaches to constructing a pie chart from any given data
(A) Degree Approach: The central angle in a circle represents 360o, so any part or segment in a pie chart is calculated as a proportion of 360o.
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(B) Percentage Approach: In this case, any part or segment in a pie chart is calculated as a part of 100%.
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Conversion of degree approach to percentage approach:
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If we convert the same pie chart into the degree format, we will be required to do the following conversions:
Total = 100%
Hence, 1% = 3.6o
Central = 10% = 36o
North = 20% = 72o
South = 25% = 90o
East = 15% = 54o
West =30% = 108o
Question for Pie Charts
Try yourself:The central angle of a sector is 72o. What percentage of the circle is comprised by the sector?
Explanation
The arc length of a sector, in degrees, is equal to the central angle. The total number of a degrees of a circle is 360. Therefore, we can use a proportion to calculate the percentage.
72/360 = x/100
7200 = 360x
20 = x
Therefore, 20% of the circle comprises the sector..
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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 build up 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.
Example: Following is the cost analysis of a book “Guide to Digital Marketing”.
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What is the central angle showing the cost of paper?
(a) 42.8o
(b) 32.6o
(c) 36.8o
(d) 57.6o
Solution: Percentage of paper cost in total cost - 16%
We know that the sum of angles in pie chart is 100o
Hence, Required Angle = (16/100 × 360) = 57.6o
Question for Pie Charts
Try yourself: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
Explanation
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.(4,62,000/500) = Rs.84.
So, marked price = 140% of Rs.84 = Rs.117.60.
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