### Theory:

Let us try to analyze the probable data to the conditions given below:

1. The number of students present in the school.

2. The age group of students studying in an Engineering college.

After data collection, we found out that there are $$1000$$ students present in a school, and the age group of students studying in an Engineering college is between ages $$17$$ and $$21$$.

What do you think is the difference between the two types of data collected?

The answer to the number of students in a school is a whole number which is ungrouped data or discrete data. The answer to the age group of students studying in an Engineering college is limited to ages between a minimum value and a maximum value which is a grouped data or continuous data.
Ungrouped or discrete data
When the data collected is a whole or exact measurement, it is ungrouped data or discrete data.
Example:
1. The number of books in a library.

2. The number of bikes in a showroom.
Grouped or continuous data
A grouped or continuous data is any value between a minimum value and a maximum value. In other words, continuous data will have values from a particular range. This type of data can be tabulated in the form of a frequency distribution table.
Example:
1. The age group of cricketers in India.

2. The number of floors in government buildings.
Range
The difference between the highest value and the smallest value in a set of data is the range.
Example:
Consider the following set of data $$2$$, $$7$$, $$8$$, $$6$$, $$10$$, $$5$$, $$6$$, $$8$$, $$2$$.

The frequency distribution table will look like the following:

 Number Frequency $$2$$ $$2$$ $$5$$ $$1$$ $$6$$ $$2$$ $$7$$ $$1$$ $$8$$ $$2$$ $$10$$ $$1$$

The data is entered in the ascending order of entries followed by the number of times it gets repeated.

From the column 'Number', we know that the highest value is $$10$$, and the smallest value is $$2$$.

$$\text{Range} = \text{Highest value} - \text{Smallest value}$$

$$= 10 - 2$$

$$= 8$$

Therefore, the range of the given set of data is $$8$$.