Data Table

Data fails to convey their meaning, if they are not presented properly. When the data are presented neatly, their important characteristics are highlighted. 
There are many methods of presenting data. The two important methods are: -
(i)   Data Table
(ii)  Graphic and Diagrammatic Representation.

Data Table Definition

After classification of data, the next step is tabulation of data. It is the process of creating data table. A data table is an orderly arrangement of data in rows and columns.  Data table helps us to systematically represent the data.

Making a Data Table

Following are the rules to be followed while constructing a data table

  1. Data table must be neat, compact and clear
  2. Data table should not be over loaded with unnecessary details
  3. The contents must be arranged in correct order
  4. Proper titles must be must be given to each part of the data table
  5. Heading must be self-explanatory so that even laymen can understand the contents in the table.
  6. If required, we have to include row headings also.
  7. As for as possible abbreviations should not be used
  8. Do not use ditto marks
  9. Contents must be arranged so that we can compare the data easily.

Parts of a Data Table

The important parts of the data table are
  • Table number
  • Title of the table
  • Row heading and column heading
  • Body
  • Head note
  • Foot note
  • Source of the table

Uses of Data Table

Uses of Data table

(i)    It simplifies the complexity
(ii)    It facilitates comparison
(iii)    It reveals the nature of relationship between the variables.
(iv)    It helps further analysis of the data.
(v)    It helps us to eliminate the unnecessary details, which are collected.

Limitations of Data table


  • It can be difficult to see numerical relationships and patterns. A graph may make these clearer.
  • When clumping information into bands, there is no indication of how many are in each category


Example of a blank data table
Following is a blank data table showing the population according to age and sex

          Age          
                                         Sex                                  
            Male    
               Female 
 0-20    
 20-40    
 40-60    
 60-80    
 80-100    
 Total    

One and Two Way Table

According to the number of characteristics or variables  presented, tables are divided into 3.
  • One way table or one variable table
  • Two way table or two variable table
  • Manifold table

One way table or One variable table
In One way table one characteristic or variable is presented. One way tables are also known as simple table or one variable table.

Example: -
One way table

                Year                                              Literacy                              
 
        Illiterate               Literate
 2005   12
    15
 2006   23     34
 2007   45
    65 

In this case data are presented based on a single characteristic or variable “literacy”.


Two way table or two variable table
When there are two characteristics or variables are presented, it is known as two way table. Two way tables are also known as two variable tables

Example: -

Two way table

                  Age                   
                           Literacy                               
           Literate
               literate 
 0-10       5
    12
 10-20      17
    13
 20-30 
    35
    5

In this case two characteristics or variables are age and literacy are presented.


Manifold table
When the number of characteristics is more than two, the table is known as manifold table.

Example: -
Manifold

                Age                
                 Literate                 
                   Illiterate             
          Male     
       Female         Male          
           Female    
0-10
35
45
56
 45
 10-30  25  65  75  85
 30-50  78  25  86  56
 50-100  15  22  14  25

In this case three characteristics or variables are age, sex and literacy are presented.

Graphing Data

Graphic and diagrammatic representations present dry and uninteresting data in an appealing and interesting way.  It simplifies the complexity of data and makes them easily intelligible.

Uses of graphs and diagrams


(i)    Graphs and diagrams help in presenting data in a simple and attractive form.
(ii)    Graphs and diagrams are useful for comparison
(iii)    They saves much time in understanding data.
(iv)    Graphs can be used to find measures like median, mode, quartiles etc.
(v)    They can be understood without mathematical calculations.

Limitations

  • Only limited amount data can be represented on a graph or diagram.
  • They show only approximate values.
  • They require more time to construct.
  • They are not capable of further algebraic treatment.

Types of Graphs and Diagrams

There are many types of diagrams.  They are bar diagram, Line diagram, Area diagram, Pie charts in all these graphs either the magnitude or area is taken proportional to the value of the variable.      Graphs are used to represent frequency distribution using relationship between two variables. Different types of graphs are Histogram, Frequency polygon, frequency curve,  gives etc.

Frequency Distribution

A frequency table is an orderly arrangement of data classified according to the magnitude of observations.  When the data are grouped into classes of appropriate size indicating the number of observations in each class we get a frequency distribution.

Example: -
The following is an example of a frequency table:-

 Marks   Number of students 
  0-5    5
  5-10   4
 10-15  12
 15-20  18
 20-25  18
 25-30  6
 30-35     17
 35-40   24
 40-45  12
 45-50  4
     
 
Central tendency

A Measure of Central Tendency or an average is a figure that represents the whole group.  It is a value lying between the minimum and maximum values of the series and is generally located in the middle of the series.  Hence it is called measure of central tendency.

Mean of the frequency distribution


If $x_{1},x_{2},…x_{n}$ are the n mid values  and $f_{1},f_{2},…f_{n}$ are the corresponding frequencies in the frequency distribution, then the mean is given by
$\bar{x}=\frac{f_{1}x_{1}+f_{2}x_{2}+....+f_{n}x_{n}}{N}=\frac{\sum fx}{N}$ where N = $\sum f$.

Example:  Find the mean of the following data
Class:    20-25    25-30    30-35    35-40    40-45    45-50    50-55
F      :      10         12         8         20         11         4           5

Solution 

            Class                           f                           x                                 fx                  
 20-25  10  22.5  225
 25-30  12  27.5  330
 30-35  8  32.5  260
 35-40  20  37.5  750
 40-45  11  42.5  467.5
 45-50  4  47.5  190
 50-55  5  52.5  262.5
 Total  70    2485

$\sum fx$ = 2485, $\sum f$ = 70

Mean is given by  $\bar{x}$ = $\frac{f_{1}x_{1}+f_{2}x_{2}+....+f_{n}x_{n}}{N}$ = $\frac{\sum fx}{N}$
                                     = $\frac{2485}{70}$
                                     = 35.5
Answer Mean = 35.5