Statistical Triad - Groups, Data, Inference
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Statistical Triad - Groups, Data, Inference

Figure 118.1 illustrates the conceptual essence of statistic.
(a) What is statistics?

The strings: S7P6A64 (Grouping - Multi-criteria).

The math:
Pj Problem of Interest is of type grouping (multi-criteria). Grouping is at the heart of statistics. The grouping may be permutational or combinational, single criterion or multi-criteria grouping.

(a) Only 7 types of problems (P1, P2, P3, P4, P5, P6 and P7) constitute the core of existential problems. However, these problems are variedly manifested in form and complexities. Social and biological problems are replete with such complexities. The search for a reliable method for extracting pertinent information from complex problems not amenable to precise solutions was the impetus for the discovery of statistics which is in essence the quantification and extraction of non-deterministics (probabilistic) information from a population of interest. In other words, statistics exists because of lack of precise information.

John Graunt (1620-1674) is credited with the founding of statistics. Graunt's 1662 book Natural and Political Observations ... upon the Bills of Mortality initialized the quantitative inquiry into the social sciences. William Petty (1623-1685), L.A.J Quetelet (1796-1874), Francis Galton (1822-1911) and Karl Pearson (1857-1936) were early contributors and developers of statistics. Today, statistical information is ubiquituous.

(b) Grouping: no population, no statistics. It is from a given population that a group of interest is extracted. Graunt knew this very early on when just out of curiosity, he was studying the death records in English cities. He categorized the percentages of death due to accidents, suicides, and various diseases and noticed that the variations were not significant.
Data: the purpose of the grouping is to collect and analyze data of interest. Graunt was interested in percentages of death due to accident, suicides and various other diseases.
Inference: the purpose of the data collection and analyses is to extract quantitative information (not otherwise available by standard scientific method) about the groups of interest.

A primary characteristic of statistics is that it provides reliable information about large groups and do not provide definite prediction about any individual case.

Math

Blessed are they that have not seen, and yet have believed. John 20:29