Draw a pie-diagram representing the relative frequencies
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 $=\left(\right.$ component value $/$ sum of component values $\left.\times 360^{\circ}\right)$

Here, total amount = 100.1%

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

ItemAmount (in %)Sector angle
Class I12.612.6/100.1 x 360 = 45.3
Class II18.218.2/100.1 x 360 = 65.5
Class III17.517.5/100.1 x 360 = 62.9
Class IV20.320.3/100.1 x 360 = 73
Class V2.82.8/100.1 x 360 = 10.1
Class VI4.24.2/100.1 x 360 = 15.1
Class VII9.89.8/100.1 x 360 = 35.2
Class VIII14.714.7/100.1 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 73o. Draw a sector with the central angle 73o 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.​​

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