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: $α_{i} = f_{i} \cdot \frac{360^{\circ}}{N}$

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:

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:

imagen