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 \(8\).