Relation of Venn diagram and n way frequency table!!

We know the Venn diagram is a diagram that shows all possible logical relations between a finite collection of different sets. It is a schematic representation of the elements in a set or a group. And on the other hand frequency table represents the data in tabular form.

We can easily convert the Venn diagram in an n way frequency table and vice versa.

Suppose there are 60 students in a class. The Venn diagram shows how many students like coffee, like tea, like both, or neither. We can easily convert this into a 2-way frequency table.

First, if we draw the table it will look like as:

The first cell represents the numbers where both tea and coffee are liked. The 2nd cell represents the numbers who like coffee but not tea. On the other hand, 3rd cell represents the numbers who like tea but not coffee. And the last cell, the 4th cell represents numbers who neither like coffee or tea.

From the Venn diagram, we see that 5 students like both coffee and tea, so we can put the 5 in the first cell. 20 students like only coffee and 25 students like only tea. So we can put them on the 2nd and 3rd cell respectively. And on the last cell, we can put 10 as numbers of students who neither like coffee or tea. So after finishing we can see our table as:

From this, we can find row total, column total, relative frequency, probability, and much more things.