Theory:

Before editing the data, the data is collected and not used for any purpose, then the data is called as Raw data.
Example:
Observe the weights of \(26\) students in a classroom.
 
\(31\), \(32\), \(52\), \(60\), \(37\), \(49\), \(42\), \(56\), \(43\), \(55\), \(72\), \(84\), \(67\), \(75\), \(44\), \(41\), \(59\), \(57\), \(28\), \(78\), \(66\), \(81\), \(88\), \(86\), \(56\)
 
We can see that the data is very large, and the reader find it difficult to understand it. From the data, we find it hard to find the number of times \(56\) repeats.
 
Hence, let us group the given data in order to read the data easier.
 
Class intervalWeight of sudents
\(20 - 29\)\(28\)
\(30 - 39\)\(31\), \(32\), \(37\)
\(40 - 49\)\(49\), \(42\), \(43\), \(44\), \(41\)
\(50 - 59\)\(52\), \(56\), \(55\), \(59\), \(57\), \(56\)
\(60 - 69\)\(60\), \(67\), \(66\)
\(70 - 79\)\(72\), \(75\), \(78\)
\(80 - 89\)\(84\), \(81\), \(88\), \(86\)
 
From the above data, we can easily find the highest number and the lowest number and how many times the number \(56\) repeats.
 
If we need to know how many students have a weight less than \(60\), we need to alter the above table. Instead of writing the weights of each student, let us write the number of students have weights between the respective class intervals. Thus, we have:
 
Class intervalNumber of sudents
\(20 - 29\)\(1\)
\(30 - 39\)\(3\)
\(40 - 49\)\(5\)
\(50 - 59\)\(6\)
\(60 - 69\)\(3\)
\(70 - 79\)\(3\)
\(80 - 89\)\(4\)
 
This table gives the number of students in each class, which tells us the number of items an item occurs in the required interval. This number of times an item occurs in the required interval is called as frequency and the table is called as frequency table.
The number of times an entry repeats itself in that set of data is called as frequency of that class.
We can also use tally marks to represent the frequencies. The speciality of the tally mark is once it reaches the \(4\) it strikes out and becomes as \(5\), so whenever the tally mark is a strikeout, we should read it as \(5\).
For the interval \(80 - 89\), the frequency is \(4\), and we can represent it in tally mark as Figure 13.png. Similarly, for the interval \(40 - 49\), the frequency is \(5\) and we represent in tally mark as Figure 14.png.
 
Now, the frequency table using tally marks can be written as:
 
Class intervalTally marksNumber of students
\(20 - 29\)Figure 10.png\(1\)
\(30 - 39\)Figure 12.png\(3\)
\(40 - 49\)Figure 14.png\(5\)
\(50 - 59\)Figure 14.png Figure 10.png\(6\)
\(60 - 69\)Figure 12.png\(3\)
\(70 - 79\)Figure 12.png\(3\)
\(80 - 89\)Figure 13.png\(4\)