Question

consider the following statements:
$1$) Pie diagrams are suitable for categorical data.
${\text{2)}}$ The arc length of a sector of a pie diagram is proportional to the value of the component represented by the sector.
Which of the statements given above is/are correct?
${\text{A)}}$ $1$ Only
${\text{B)}}$ $2$ Only
${\text{C)}}$ Both $1$ and $2$
${\text{D)}}$ Neither $1$ nor $2$

Answer 1

Pie chart is a circular representation of the given data which is used to categorize data. The arc length of the pie chart is proportionate to its value. Finally we discuss the example to clarify to conclude the required answer.

Complete step-by-step solution:
In this question we have to discuss the pie diagram and length of a sector which is used to draw a pie chart and it uses.
First we define the pie graph as follows:
Pie graph is a very commonly used type of graph to represent things in circular form which is actually divided into different pieces or slices to represent the numerical values of the data.
It is commonly used to categorize data. In the pie graph, the pieces length is known as arc length. The data given will be converted into degrees and represented in the table.
Now we discuss about the arc length of a pie diagram as follows:
So, the arc length of a sector of a pie diagram is proportional to the numerical value represented in the given data
Example: The given data is:

Monday	Tuesday	Wednesday	Thursday	Friday
$38\%$	$15\%$	$8\%$	$31\%$	$8\%$

From the given pie diagram, we can see that the arc length of the pie graph is proportional to the values given as the data.
Therefore the given statements both are correct.

The correct answer is ${\text{C)}}$ both $1$ and $2$

Note: It is common that all the graphical representations are suitable for categorising data. Among them, the pie chart is more suitable because of this circular structure. With that feature pie chart is more suitable for comparing and categorising.