Showing posts with label STATISTICS. Show all posts
Showing posts with label STATISTICS. Show all posts

Wednesday, 17 October 2012

Types of table in statistic?



Types of table:

Statistical tables are classified in two types:

i.                        General purpose table:

General purpose table also known as primary or reference table contain detailed statistical information about the variety of problems and published for reference purposes. These tables are available to others, who want to use them for analysis of special problems. These tables contain primary information’s and do not contain computed measures such as rate, ratios, averages etc.

ii.                        Special or specific purpose table:

Special purpose table also known as text table or summary table or analytical table are tables used to analyses the special problems under study. E.g. production figure of a particular industrial unit for a number of years or the figure relating to its profit would give us specific or special purpose table.

One way or simple table:

A table in which observations are classified according to single characteristic (variable) is called the one way or simple table. E.g. marks obtained by students in statistics are shown below.

Marks obtained by students in statistics:

Marks
No. of student
40-50
14
50-60
26
60-70
30
70-80
20
80-90
10
Total
100
           











Two way or double table:

A table which gives information’s about the two inter-related characteristics (variable) is called two ways or double table. The marks obtained and sex wise distribution of 100 students is an example of two way table and is shown below.

Marks obtained by students in statistics (sex wise):

                                                 No. of student
Marks
Male 
female
total
40-50
8
6
14
50-60
16
10
26
60-70
14
16
30
70-80
12
8
20
80-90
6
4
10
Total
56
44
100
                                                               
Three way tables:

A table which gives information’s about the three inter-related characteristics (variable) is called three way tables. The marks obtained by students sex wise and on the basis of residential status is an example of three way table. Consider the following.

Mark obtained by students in statistics sex wise and on the basis of residence:

Marks

                                                                No.  of students
Total
Male

Female
Total
Hostellers
Day scholar
Total
Hostellers
Day scholar
total
hostellers
Day scholar
40- 50
4
4
8
4
2
6
8
6
14
50 – 60
10
6
16
5
5
10
15
11
26
60 – 70
8
6
14
9
7
16
17
1
30
70 – 80
7
5
12
5
3
8
12
8
20
80 – 90
5
1
6
2
2
4
7
3
10

34
22
56
25
19
44
41
41
100

Relative frequency distribution,Relative cumulative frequency distribution and Bivariate frequency distribution


Relative frequency distribution:

A table in which the frequency of each class is divided by the total frequency of all the classes is called relative frequency distribution. When the relative frequencies are expressed as a percentage, than it is called percentage relative frequency distribution. It is important to note that the sum of the relative frequencies of all classes should equal to one 1 or 100%.

Relative cumulative frequency distribution:

A table in which the cumulative frequency of each class is divided by the total frequency of all classes is called relative cumulative frequency distribution. Or %age relative cumulative frequency distribution. It is to be noted that relative cumulative frequency of last class should equal 100.

Question:

From the data given below construct relative frequency distribution and percentage relative frequency distribution.

Marks:          10 – 20   20 – 30   30 – 40   40 – 50   50 – 60   60 – 50   
Frequency:       5             16            31            28            19           10 

Sol:

marks
F
%age relative frequency
10 – 20
5
5/109 x 100 = 4.6
20 – 30
16
16/109 x 100 = 1.7
30 – 40
31
31/109 x 100 = 28.4
40 – 50
28
28/109 x 100 = 25.4
50 – 60
19
19/109 x 100 = 17.4
60 – 70
10
10/109 x 100 = 9.2

109
100

From the above table we can read that 4.6% of the students obtained 10 or more but less than 20 marks 25.7% of the students obtained 40 or more but less than 50 marks etc.

Question:

Construct the relative cumulative frequency distance and %age relative cumulative frequency distribution from the following data.

Marks:                      0 - 10 10 – 20   20 – 30   30 – 40   40 – 50   50 – 60  
Frequency:                 8            12            24            18           10             5

Sol:

Marks
F
Cumulative freq (less than type)

0 - 10
8
8
8 ÷ 77 x 100 = 10.4
10 – 20
12
8 + 12  = 20
20 ÷ 77 x 100 = 25.9
20 – 30
24
8 + 12 + 24 = 44
44 ÷ 77 x 100 = 57.1
30 – 40
18
8 + 12 + 24 + 18  = 62
62 ÷ 77 x 100 = 80.5
40 – 50
10
8 + 12 + 24 + 18 + 10 = 72
72 ÷ 77 x 100 = 93.5
50 – 60
5
8 + 12 + 24 + 18 + 10 + 5 = 77
77 ÷ 77 x 100 = 100

77



From the above table we can read that 10.4% of the students obtained less than 10 marks, 80.5% of the students obtained less than 40 marks etc.

Bivariate frequency distribution:

The frequency distribution con structured so far for a single variable is called univarite frequency distance. But in many problems we deal with two variables, the frequency distribution con structured for such variables is called the bivariate frequency distribution.

There rules for construction of bivariate frequency distribution is exactly the same as that of univarite frequency distributions. Since two variables are studied at the same time, therefore the classes for one variable are arranged in rows and that of the second variable in columns.
 

Total Pageviews

Contributors