Diagram of sectors

The diagram of sectors is usually used for qualitative variables, but it can also be used to represent discrete data.

It consists on dividing a circle so that the most frequent values have bigger sectors. To calculate the angle of the sector of each value we use the following expression: $$\displaystyle \alpha_i=f_i \cdot \frac{360^\circ}{N}$$

where $N$ is the number of data, and $f$ is the frequency corresponding to the angle alpha.

The following table shows the value of the angle for every number of brothers using this example:

$15$ students answer the question of how many brothers or sisters they have. The answers are $$1, 1, 2, 0, 3, 2, 1, 4, 2, 3, 1, 0, 0, 1, 2$$ Then, we can construct a table of frequencies

No. of brothers Angle
$0$ $72^\circ$
$1$ $120^\circ$
$2$ $96^\circ$
$3$ $48^\circ$
$4$ $24^\circ$

Notice that they add up to $360^\circ$. And the sectors diagram is:

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Practice exercises