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Statistics Homework Helper

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Who needs mathematical statistics:


- Scientists who work with the results of experiments and studies and try to interpret them correctly.
- Sociologists who study public opinion, analyse and group results.
- Analysts who work across business sectors: assessing performance, building models, identifying trends and proposing
hypotheses.
- Marketers who need to understand and be able to work with statistical data in order to build advertising strategies
based on the available information.
- Data analysts who need to be able to process large amounts of information, and statistics help with this.
- Economists who work with financial indicators, including statistics.
- Engineers, doctors and other professionals whose work may involve calculations and aggregation of data.

What mathematical statistics is used for:

- To properly collect and process statistical data.
- To describe large amounts of data that express phenomena, from the results of a physical experiment to a poll or
information about visits to a website.
- Presenting data in graphs or tables.
- To predict and test hypotheses - assumptions that can be confirmed or disproved using statistical data.
- To get rid of errors that may be due to incorrect collection, processing or interpretation of data.
- To calculate possible deviations of the result from the truth.


What terms does statistics work with:

1. General population

A population of all possible outcomes that could be obtained under the same conditions. It is impossible to measure the general population; its size tends to infinity. But mathematical statistics uses methods that help us understand how to describe it - it uses sampling.

2. Sampling

The data that is obtained from observations. The sample size is finite and limited by the criteria - the methods of selection. In this way, a set of choices are selected from the general population, from which it is theoretically possible to infer the whole. For example, if the general population is the opinion of absolutely all the people on an issue, the sample is the results of a survey on it.

3. Representativeness

A concept that tells how representative a sample is, whether or not it has a realistic distribution of options. A sample is considered representative if it includes many parameters and reliably represents the general population.

For example, if the sample includes only the elderly, it will not be representative of all age groups. If an older age group was studied, then the general population would be all older persons. In that case, the sample may be representative.

Representativeness is usually obtained through randomisation - objects or people are selected randomly from the general population. This results in a sample of many different variations. If this is not possible, then representativeness is approached in other ways.

4. Distribution

The indicator is often described by mathematical formulas. It shows the frequency with which different variants occur in a sample. As a result, it is possible to infer which variants of the data outnumber which variants - what is more or less common within the sample. If it is representative, it will help to draw conclusions about the general population as well.

5. Visualization

To make the results easier to understand, they are visualized. Usually histograms of the distribution are plotted - charts with bars that vary in size according to the value. But other types of visualization are also used: dot plots, pie charts, and so on.
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