The frequency is the number of times a data has been repeated. So
the table which contains frequency and data is called a frequency distribution table or simply a frequency table.
Frequency Table For Discrete Data:
Example: Let’s observe the marks secured by 20 students in a
math test of 20 marks.
10, 8, 9, 8, 10, 10, 11, 12, 14, 15, 8, 9, 7, 8, 10, 10, 11, 12,
10, 8
The frequency distribution table of the above data is given
below:
Marks 
Frequency 
7 8 9 10 11 12 14 15 
1 5 2 6 2 2 1 1 

N = 20 
Frequency Table For Group (Continuous) Data:
When the number of observations is a large amount of data which
are converted into a compact form, we organize it in groups. These groups are
called class intervals. We should make groups or classes of the same size. The
difference between the upper limit and lower limit of a group is called class size.
Consider the following data showing the marks of 30 students in
the first term examination.
23, 29, 40, 15, 30, 35, 45, 48, 25, 5, 16, 22, 18, 33, 42, 46,
23, 36, 31, 26, 24, 37, 42, 20, 19, 41, 28, 38, 29, 17
Marks 
Frequency 
0  10 10  20 20  30 30  40 40  50 
1 5 10 7 7 

N = 30 
Frequency Distribution Table For a Large Number of Data
For a large number of data, to draw a frequency table, we should
use the following steps:
Step 1: Identify the smallest data and largest data.
Step 2: Divide the data into an appropriate class interval of the same
size
Step 3: Common data always belongs to the higher class e.g. in 1020
and 2030, 20 lies in 2030.
Step 4: Count the data and write tally bars in a frequency table.
Cumulative frequency table
Cumulative frequency is a continuous frequency distribution in
which frequencies are cumulated either in ascending or descending order. Look
at the following example to be more clear about the cumulative frequency.
Marks 
10 
20 
30 
40 
50 
60 
No. of students 
2 
5 
4 
7 
3 
6 
Cumulative frequency table:
Marks 
No of students (f) 
Cumulative frequency (C.F.) 
10 20 30 40 50 60 
2 5 7 4 3 6 
2 2+5=7 7+7=14 14+4=18 18+3=21 21+6=27 

N = 27 

From the above table, it is clear that the cumulative frequency
is the sum of the frequencies up to the corresponding class.
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Workout Examples
Example 1: Represent the following data in a frequency distribution table.
15, 10, 16, 9, 7, 8, 9, 10, 15, 10, 8, 4, 7, 8
Solution:
Here,
Frequency distribution table,
Data 
Frequency 
4 7 8 9 10 15 16 
1 2 3 2 3 2 1 

N = 14 
Example 2: Represent the following data in a frequency distribution table by
making appropriate class intervals.
4, 7, 12, 15, 50, 22, 25, 27, 29, 33, 39, 44, 47, 18, 51, 31, 20, 21,
41, 36
Solution:
Here,
Frequency distribution table,
Data 
Frequency 
010 1020 2030 3040 4050 5060 
2 3 6 4 3 2 

N = 20 
Example 3: Represent the following data in a cumulative frequency
distribution table.
8, 7, 9, 16, 10, 10, 12, 15, 15, 12, 8, 7, 10, 10, 10, 12, 12, 14, 15,
18
Solution:
Here,
Cumulative frequency distribution table,
Data 
Frequency 
C.F. 
7 8 9 10 12 14 15 16 18 
2 2 1 5 4 1 3 1 1 
2 2+2=4 4+1=5 5+5=10 10+4=14 14+1=15 15+3=18 18+1=19 19+1=20 

N = 20 

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distribution table here.
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