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PRACTICE 1: Basic Concepts of Mathematical Statistics

Plan:

1. Basic concepts of mathematical Statistics

2. Concepts of descriptive and inferential statistics

3. Concepts of population, sample, and representativeness

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"Mathematical statistics is a branch of mathematics that develops methods for recording, interpreting, and analyzing data obtained from observations and research, with the aim of constructing probabilistic models of mass random phenomena."

Mathematical statistics is applied in the following processes:

-Summarizing research results;

-Finding correlations between obtained data;

-Proving the validity of methodologies and methods;

-Making statistical forecasts;

-Confirming or rejecting hypotheses;

-Discovering fundamentally new knowledge;

-Planning effective research;

-Developing new methodologies.

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Descriptive Statistics

Descriptive statistics is a set of empirical methods used for interpreting, classifying, and visualizing obtained data (including calculations of selected characteristics, charts, and diagrams). In descriptive statistics, the probabilistic nature of the data is not taken into consideration.

Descriptive statistics is used in the following cases:

-Data collection;

-Data categorization;

-Data summarization;

-Data presentation.

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Inferential Statistics

Inferential statistics is a technique based on the mathematical theory of probability that defines the population and its representativeness.

The task of inferential statistics consists of proving how closely two samples represent their respective populations, as well as verifying whether the results obtained from a specific sample can be applied to the results of the entire population from which that sample was drawn.

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Population

The population embodies all the qualities and characteristics that interest the researcher. A psychologist-researcher always selects a specific group from a larger pool of individuals. In statistics, this entire group is called the population. Population variables are denoted by the symbol "N".

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Sample

A sample refers to the elements of subgroups—subjects, respondents, or participants—selected from the population to conduct research. The sample size is denoted by the symbol "n". In statistics, samples are classified as small (n < 30), medium (30 < n < 100), and large (n > 100).

Representativeness of the Sample