Introducing soft computing statistical measures: very useful & significant measures by algebraic approach
Ranjit Biswas · International Journal of Algebra · 2014
In the subject Statistics, the term “universe” refers to the total of the items or units in any field of enquiry, whereas the term “Population” refers to the total of items about which information is desired by a statistician (or by the statisticians). A population may not be just a collection of real number data, in general. Consequently, we define population into two categories: R-Population and NR-Population. If a population is of real number data only, it is of category ‘R-Population’, and if a population does not fall into the category of ‘R-Population’ then it is of the category ‘NR-Population’. Thus a ‘NR-Population’ could be a collection of any type of data, viz. collection of sounds from a bus horn, collection of a large number of handwritten characters of the English character “A”, collection of 100 paints of beautiful ‘Tajmahal’ by 100 number of under-9 children, etc. The main concern addressed in this paper is that the classical measures of statistics, in particular the three fundamental measures : mean (arithmetic mean), median and mode are undefined measures for NR-population data. But there are a lot of analysis, survey, estimations, conclusions, etc. being carried out by the analysts for various important objectives over such type of NR-populations in real life. The failure of these classical measures to play any role over NR-populations has been a hidden truth so far to the statisticians or analysts. In this paper the author introduces a new direction for formulating a number of new statistical measures for both kind of population (not