FREQUENCY DISTRIBUTION
Statistics of Class 9
FREQUENCY DISTRIBUTION
The marks scored by 30 students of IX class, of a school in the first test of Mathematics our of 50 marks are as follows:
|
6 |
32 |
10 |
17 |
22 |
28 |
0 |
48 |
6 |
22 |
|
32 |
6 |
36 |
26 |
48 |
10 |
32 |
48 |
28 |
22 |
|
22 |
22 |
28 |
26 |
17 |
36 |
10 |
22 |
28 |
0 |
The number of times a mark is repeated is called its frequency. It is denoted by f.
|
Marks obtained |
Tally mark |
Frequency |
Marks obtained |
Tally mark |
Frequency |
|
0 |
II |
2 |
26 |
II |
2 |
|
6 |
III |
3 |
28 |
IIII |
4 |
|
10 |
III |
3 |
32 |
III |
3 |
|
17 |
II |
2 |
36 |
II |
2 |
|
22 |
IIII I |
6 |
48 |
III |
3 |
Above type of frequency distribution is called ungrouped frequency distribution. Although this representation of data is shorter than representation of raw data, but from the angle of comparison and analysis it is quite bit. So to reduce the frequency distribution, it can be classified into groups is following ways and it is called grouped frequency distribution.
|
Class |
Frequency |
|
0 – 10 |
8 |
|
11 – 20 |
2 |
|
21 – 30 |
12 |
|
31 – 40 |
5 |
|
41 – 50 |
3 |
(a) Types of Frequency Distribution:
Statistical methods like comparison, decision taken etc. depends of frequency distribution. Frequency distribution are of three types.
(i) Individual frequency distribution : Here each item or original price of unit is written separately. In this category, frequency of each variable is one.
e.g. Total marks obtained by 10 students in a class.
|
S. No. |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
|
Marks obtained |
46 |
18 |
79 |
12 |
97 |
80 |
5 |
27 |
67 |
54 |
(ii) Discrete frequency distribution : When number of terms is large and variable are discrete, i.e., variate can accept some particular values only under finite limits and is repeated then its called discrete frequency distribution. For example the wages of employees and their numbers is shown in following table.
|
Monthly wages |
No. Of employees |
|
4000 |
10 |
|
6000 |
8 |
|
8000 |
5 |
|
11000 |
7 |
|
20000 |
2 |
|
25000 |
1 |
The above table shows ungrouped frequency distribution the same facts can be written in grouped frequency as follows :
|
Monthly wages |
No. of employees |
|
0-10,000 |
23 |
|
11,000-20,000 |
9 |
|
21,000-30,000 |
1 |
|
|
If variable is repeated in individual distribution then it can be converted into discrete frequency distribution. |
(iii) Continuous frequency distribution : When number of terms is large and variate is continuous. i.e., variate can accept all values under finite limits and they are repeated then it is called continuous frequency distribution. For example age of students in a school is shown in the following table :
|
Age (in year) |
Class |
No. of students |
|
Less than 5 year |
0-5 |
72 |
|
Between 5 and 10 y ear |
5-10 |
103 |
|
Between 10 and 15 year |
10-15 |
50 |
|
Between 15 and 20 year |
15-20 |
25 |
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|
Continuous frequency distribution is generally represented in form of grouped frequency distribution and variety is continuous in i, so 0 - 5, 6 - 10, 11 - 15, 16 - 20 types of classes cannot be made here. If such classes are made in the table then students of age 5 to 6 year or 10 to 11 year or 15 to 16 years cannot be classified. if such type of classes are given then they should be made continuous by following methods. Half of the difference between classes should be added to the upper limit of lower class and subtracted from lower limit o upper class. Thus the classes 0 - 5.5, 5.5 - 10.5, 10.5 - 15.5, 15.5 - 19.5 are obtained which are continuous. |
