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.
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'.
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 are categorical data. They are non-numeric in nature and cannot be measured. Examples are sex, religion and place of birth.
Quantitative data are numerical in nature and can be measured.
Examples are age, members in the family, income and savings.
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 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 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 can take any numerical value within a specific interval e.g. height in centimetres; weight in kilograms; income in rupees.
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.
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.
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.