Frequency Distribution Table
The frequency is the number of times of repetition of
data. So the table which contains frequency and data is called a frequency distribution table or simply 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
|
For
group (continuous) data:
When the number of observation is a large amount of
data which are converting into a compact form, we organize it in groups. These
groups are called class intervals. We should make group or classes of the same
size. The difference of 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
|
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 in the same size
Step 3 :Common data always
belongs to the higher class e.g. in 10-20 and 20-30, 20 lies in 20-30.
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 accumulated 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
|
From the above table, it is clear that the cumulative
frequency is the sum of the frequencies up to the corresponding class.
Workout Examples
Example 1: Represent the following data
into 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
|
Example 2: Represent the following data
into a frequency distribution table by making appropriate class interval.
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
|
0-10
10-20
20-30
30-40
40-50
50-60
|
2
3
6
4
3
2
|
Example 3: Represent the following data
into 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
|
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questions or problems regarding the frequency distribution table here.
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