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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: