## Reference 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.

- Find the sum total of all the observations.
- Convert the data set into corresponding degrees in the circle by using the formula:

Total of observations = 360^{0}(Since total angle formed by a circle = 360^{0})

- It should noted that the sum of the angles converted should be equal to 360
^{0} - Draw a circle of appropriate size by the help of compass.
- Draw a radius at any point on the circle. (Better at 12 O’ clock position).
- Take the radius drawn as the baseline and draw the successive angles one after another in the circle by the protractor.
- 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 region | No. of schools |

Eastern Central Western Mid-western Far-western | 165 325 190 49 60 |

Total | 789 |

**Solution:**

Calculation of angles for pie-diagram

Development region | No. of schools | Angle (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 |

Total | 789 | 360 |

Above diagram is the example of Pie-Diagram.