Quantitative Aptitude Data Interpretation Study Material
Data may be presented in the form of tables, graphs or diagrams. Tables consist of precise numerical figures whereas diagrams give only an approximate idea. However, diagrams and graphs have the advantage of showing trends in the data. While there is no clear line of demarcation between diagrams and graphs, we may note the following distinction between them :
(а) A graph represents a mathematical relationship whereas a diagram does not.
(б) Diagrams do not add anything to the data while graphs are useful in statistical analysis.
(c) Graphs are considered more appropriate than diagrams for presenting frequency distribution and time series.
In our everyday life we come across graphs, tables and other types of numerical data in newspapers, magazines, periodicals, journals, information bulletins etc. These data may relate to the cost of living, cricket average, profits of a company, temperature of cities, expenditure in various sectors of a five-year plan and so on. For instance, if we look into a newspaper, we may find a weather report giving pertinent data about the maximum and minimum temperatures and rainfall of various important cities of India and world. .
The term “data” means “information”. However, the dictionary meaning of the term “data” is “given facts.” Data may be of two types : Primary data and Secondary data.
When an investigator collects data himself/herself with a definite plan or design in his/her mind, it is called primary data. Primary data are, therefore, highly reliable and relevant These data are original in nature and are collected by some individuals or by some institutions or agencies or research bodies. For example, data collected in a census operation by the office of the Registrar General and Census Commissioner, Ministry of Home Affairs, are primary data.
However, it is not always possible for an investigator to collect primary data due to lack of time, money and resources. Many times he/she uses the data collected by some one else, which may be in the form of published reports or official statistics collected by the Government etc. Since the same data can serve various purposes, it is, therefore, possible that the data collected by an individual are used by another for his own investigation. Thus, data which are not originally collected rather obtained from published or unpublished sources are known as secondary data. Secondary data should be used with great care since these are collected with a purpose different from that of the investigator and may lose some detail or may not be fully relevant to the investigation.
Tables
Table is often used to present a set of numerical data. It helps the person to make comparisons and draw quick conclusions. It provides the reader greater objectivity in the data. Tabular presentation makes complicated information easier to understand. Its another advantage is that one can see all the information at a glance.
Tabular presentation usually consists of a table title followed by, columns and rows containing data. While looking at the table, carefully read the table title and headings/nomenclature of the columns and the rows. The table title gives a general idea of the type and objective of the data presented. The column and row nomenclatures indicate the specific kind of information contained in them respecti vely.
We present below an example of tabular presentation of annual expenditure of 5 families during the last 4 years.
Annual Expenditure of 5 families (in Rs. Thousands)
| Years—> Families 4 | 2007 | 2008 | 2009 | 2010 |
| A | 16 | 30 | 55 | |
| B | 50 | 55 | 60 | 70 |
| C | 40 | 60 | 65 | 75 |
| D | 30 | 40 | 45 | 50 |
| E | 45 | 50 | 70 | 80 |
Meaning of Tabulation
Tabulation is one of the most important devices for the presentation of the data in a condensed and comprehensive form. It attempts to furnish the maximum information contained in the data in a minimum possible space without minimising the quality and usefulness of the data.
A statistical table is the logical listing of related quantitative data in vertical columns and horizontal rows of numbers with sufficient explanatory and qualifying words, phrases and statements in the form of titles, headings and notes to make clear the full meaning of data and their origin. Thus, a table is a systematic presentation of statistical data in horizontal rows and vertical columns according to some salient features.
Merits of Tabulation
- Tabulation is the final stage in collection and compilation of the data.
- It simplifies the data.
- It depicts trend and pattern within the data
- It provides a gateway for further statistical analysis and interpretation.
- In tabulation comparable data are kept close, so that a comparable study of these data becomes easy.
- It makes the data suitable for further Diagrammatic and Graphic representation.
- It saves time and space, as maximum information is expressed in a small space without repetition.
Parts of a Table
Though the various parts of a table depend on the nature of the data and purpose of the investigation, the following features generally, form the parts of a statistical table :
(i) Table Number: Usually placed at the top of the table either in the centre above the title or in the side of the title, it V serves to identify the table for future reference.
(ii) Heading or Title : Every table is provided with a suitable title, which usually appears at the top of the table. It
is brief, simple, unambiguous, complete and self-explanatory, so that a first hand idea of the problem can be had from it.
A title describes the nature of the data, the place of relation, the time period and the source of the data.
(iii) Head Note : It is a sort of a supplement to the title. If
required, it is given just below the title to provide additional information regarding the contents of the table. The head note is usually enclosed in brackets. For example, the units of measurement are usually expressed as head note as ‘in kilometres’, ‘in crores’, ‘in Rupees’; etc.
(iv) Columns and Rows : Columns are vertical arrangements, whereas rows are horizontal arrangements. The number of rows and columns is suitably taken in view of the data under consideration. ‘
(v) Captions : Captions are the designations for vertical columns. They are placed in the middle of the columns. They briefly express the contents of the columns.
(vi) Stubs: Stubs are the designations for horizontal rows. They are placed to the left of the rows. They briefly express the contents of the rows.
(vii) Body : The data when arranged according to the designations given in the rows and columns, form the body of the table. It contains the numerical data to be presented to the readers. In view of increasing the utility of the table, totals are genrally given for each separate category either against the rows or below the columns.
(viii) Foot Note: If some additional information regarding the data is required for their complete description, foot notes are used for this purpose. As the name suggests, they are placed at the bottom of the table.
(ix) Source Note : The source of collection of data is mentioned below the foot note so that it must be known from where these have been taken. The source note is used if the data are of secondary nature.
Types of Tables
Statistical tables are formed on the basis of purpose, originality and construction. Keeping in view’ the present pattern of questions asked in competitive exams of today we will limit ourselves to the study of tabulation on the basis of construction.
This type of tabulation can be divided into two categories, namely:
(i) Simple Tables
(ii) Complex Tables
(i) Simple Tables : In a simple table, only one attribute (quality) or speciality of the data is presented.
For example:
Number of State Bank’s Employees in Different Age Groups
| Age-Groups (In Years) |
Number of Employees |
|
Less than 25 25-35 35-45 45-55 More than 55 |
——– ——– ——– ——— ——— |
| Total |
————- |
(ii) Complex Tables : In a complex table, more than one attribute or characteristic of the data are presented.
The complex tables are of three types :
- Two-way Tables
- Three-way Tables
- Manifold Tables
- Two-Way Tables : They furnish information about two inter-related characteristics of a particular phenomenon. In these tables, caption or stub is classified into two subheadings.
For example, ’
The distribution of the number of employees in State Bank with respect to age and sex is a two-way table.
Number of State Bank’s Employees with Respect to Sex in Different Age Groups Age-Groups
| Employees (In Years) | Male | Female | Total |
| Less than 25 | |||
| 25-35 | |||
| 35-45 | |||
| 45-55 | |||
| More than 55 | |||
| Total |
- Three-Way Tables : They furnish information regarding three-inter-related characteristics of a particular phenomenon.
For example, the distribution of employees in State Bank according to sex, age-groups and grades of salary is a threeway-table.
Number of State Bank’s Employees with Respect to Sex in Different Age Groups
| Age-Groups (In Years) | Employees | Total | |
| Male | Female | ||
| Less than 25
25-35 35-45 45-55 More than 55 |
|||
| Total | |||
(c) Manifold Tables : A manifold table gives the information of a large number of inter-related characteristics of a given phenomenon. For example, the distribution of employees in State Bank according to sex, age-group, year and grades of salary is a manifold table.
Now we are fully acquainted with various types of tables and their contents. While interpreting the data given in tabular form we come across different tools of analysis namely, percentage, ratio and average etc. Now we will briefly introduce ourselves to each of these tools.
Percentage : It is a fraction whose denominator is 100 and the numerator of such a fraction is termed as rate per cent. Thus the term per cent means for every hundred. It should be noted that in common parlance, per cent and percentage are used interchangeably.