#### Question

Draw a pie-diagram representing the relative frequencies (expressed as percentage) of the eight classes as given below:

12.6, 18.2, 17.5, 20.3, 2.8, 4.2, 9.8, 14.7

#### Solution

We know:

Central angle of a component = (component value/sum of component values x 360)

Here, total amount = 100.1%

Thus, central angle for each component can be calculated as follows:

Item | Amount (in %) | Sector angle |

Class I | 12.6 | 12.6/100.1 x 360 = 45.3 |

Class II | 18.2 | 18.2/100.1 x 360 = 65.5 |

Class III | 17.5 | 17.5/100.1 x 360 = 62.9 |

Class IV | 20.3 | 20.3/100.1 x 360 = 73 |

Class V | 2.8 | 2.8/100.1 x 360 = 10.1 |

Class VI | 4.2 | 4.2/100.1 x 360 = 15.1 |

Class VII | 9.8 | 9.8/100.1 x 360 = 35.2 |

Class VIII | 14.7 | 14.7/100.1 x 360 = 52.9 |

Total = 100.1%

Now, the pie chat representing the given data can be constructed by following the steps below:

Step 1 : Draw circle of an appropriate radius.

Step 2 : Draw a vertical radius of the circle drawn in step 1

Step 3 : Choose the largest central angle. Here the largest central angle is 73^{o}. Draw a sector with the central angle 73^{o} in such a way that one of its radii coincides with the radius drawn in step 2 and another radius is in its counter clockwise direction.

Step 4 : Construct other sectors representing the other items in the clockwise sense in descending order of magnitudes of their central angles.

Step 5 : Shade the sectors with different colours and label them, as shown as in the figure below.