Angular or Pie-Diagram : Diagrammatic and Graphical Representation of Data

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angular-or-pie-diagramReference Notes
Unit: Statistics | Economics
Management: Class 11

Angular or Pie-Diagram:
Pie-diagram is an alternative representation of the data set which can be presented in sub-divided and percentage bars or rectangles. These diagrams are normally used to show the total number of observations of different types of data set inside a circle into various slices according to the magnitudes in terms of angle. Usually the largest portion of the data in a pie-diagram is shown first at 12 O’clock position on the circle, whereas other observations are shown in clockwise succession in descending order of magnitude. But they can be shown in a logical order as well. The following are the steps to construct a pie-diagram.

  1. Find the sum total of all the observations.
  2. Convert the data set into corresponding degrees in the circle by using the formula:
    Total of observations = 3600 (Since total angle formed by a circle = 3600)
    angular-or-pie-diagram-formula
  3. It should noted that the sum of the angles converted should be equal to 3600
  4. Draw a circle of appropriate size by the help of compass.
  5. Draw a radius at any point on the circle. (Better at 12 O’ clock position).
  6. Take the radius drawn as the baseline and draw the successive angles one after another in the circle by the protractor.
  7. Different shades or colors can be used to represent various sectors.

Limitations of Pie-diagram:

  • It is difficult to calculate the angles with respect to the given data in comparison the bar diagram.
  • It is difficult to construct the pie-diagram in comparison to bar diagram.
  • If there are more than 6 characteristics, it is not preferable to construct a pie-diagram.
  • In pie-diagram, negative values cannot be presented.

Example:
The HSEB affiliated schools in five development regions are given in the following table. Represent these data by a pie-diagram.

Development regionNo. of schools
Eastern
Central
Western
Mid-western
Far-western
165
325
190
49
60
Total789

Solution:
Calculation of angles for pie-diagram

Development regionNo. of schoolsAngle (in degrees)
Eastern
Central
Western
Mid-western
Far-western
165
325
190
49
60
(360/789 165 = 75.8
(360/789) 325 = 148.28
(360/789) 190 = 86.70
(360/789) 49 = 22.36
(360/789) 60 = 27.38
Total789360

pie-diagram

Above diagram is the example of Pie-Diagram.

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