Statistical Analysis and Measures of Central Tendency

Statistical Analysis and Measures of Central Tendency 

The word 'statistics' is derived from the Latin word 'status' meaning a political state. In those days, therefore, statistics was simply the collection of numerical data by the state or kings. Now, statistics is the scientific method of analysing quantitative information. It includes methods of collection, classification, description and interpretation of data. It simply refers to numerical description of the quantitative aspects of a phenomenon.

Definition of statistics

Prof Horace Secrist defines statistics as follows. 'By statistics we mean aggregate of facts affected to a marked extent by multiplicity of causes numerically expressed, enumerated or estimated according to reasonable standards of accuracy, collected in a systematic manner for a predetermined purpose and placed in relation to each other'.

According to Croxton and Cowden, 'Statistics may be defined as a science of collection, presentation, analysis and interpretation of numerical data'.

Nature of data

Statistics refers to data or facts. It means data relating to sex, religion, income, population, profit etc. The data may be broadly categorised into two as Qualitative and Quantitative data.

Qualitative data

Qualitative data are categorical data. They are non-numeric in nature and cannot be measured. Examples are sex, religion and place of birth.

Quantitative data

Quantitative data are numerical in nature and can be measured.

Examples are age, members in the family, income and savings.

Raw Data

Raw data represent numbers and facts in the original format in which data have been collected

Example for raw data:Z

The percentage marks of 50 plus two students are given below

52      61      59      55      63

83      90      81      77      74

50      45      42      46      39

29      31      29      31      30

48      52      76      36      48

70      59      77      81      83

65      33      76      92      77

29      38      52      64      86

30      29      48      54      55

64      59      72      65      64

Frequency Distribution

Frequency Distribution is a summarised table in which raw data are arranged into classes and frequencies. It is called grouped data. The grouped data can be classified into two. They are discrete data and continuous data.

Discrete data

Discrete data can take only certain specific values that are whole numbers. Example: Number of classrooms in a school, number of students in a class. Discrete numbers cannot take fractional values.

Continuous data

Continuous data can take any numerical value within a specific interval e.g. height in centimetres; weight in kilograms; income in rupees.

Sources of Data

There are two basic sources of collecting the data. They are (i) Primary source and (ii) Secondary source. If the data are collected from primary source, it is called primary data. The data collected from the secondary sources are called the secondary data.

Primary data

Data collected for the first time for a specific purpose is called primary data. They are original in character. They are collected by individuals or institutions or government for research purpose or policy decisions. Example: Data collected in a population census by the office of the census commissioner.

Secondary Data

These data are not originally collected. They are obtained from published or unpublished sources. Published sources are reports and official publications like annual reports of the bank, population census, Economic survey of India; unpublished sources are the Government records, studies made by research institutions. Example for the secondary data: Census data used by research scholars.

The census data are primary to the office of the census commissioner who collected it and for others it is a secondary data.