# Standard deviation calculator

Statistics is a branch of science dedicated to the analysis and systematization of data, as well as the expression of their quantitative and qualitative indicators in numerical form.

According to the degree of generalization, primary and aggregated statistical data are distinguished, according to the number of features - one-dimensional and multidimensional, and according to the format of organization - spatial, temporal and mixed (spatio-temporal).

Statistics is the best tool for displaying social processes and phenomena, allowing you to identify weaknesses and problem areas in time, make appropriate changes to legislation, production processes, legal norms, and so on.

Statistics, whose name comes from the Latin word status and translates as "state of affairs", has existed since the time of Ancient Rome. Then it was used to keep records of property, population censuses and compare the military potentials of warring states.

But it received the status of a science only in 1746, replacing "state studies" in Germany. The initiative belongs to the German scientist Gottfried Achenwall, who turned statistics into an academic discipline in the middle of the 18th century.

## Standard deviation

In the framework of statistics, as a science, many new indicators and values have emerged. These included the standard deviation (RMS), which is still used today to describe the spread of values in a data set about their mean value.

Essentially, RMS is a measure of variability that describes how much data from one array diverges from each other. It is widely used in economics and finance, in engineering, and in many other branches of science.

According to the official definition, the standard deviation is an indicator of the dispersion of the values of a random variable relative to its mathematical expectation. In turn, the mathematical expectation is an analogue of the arithmetic mean, but with an infinite number of outcomes.

In simple terms, the lower the standard deviation, the more accurately the collected data reflect reality. Conversely, a high standard deviation indicates the ambiguity of the collected statistical information. In addition, RMS allows you to identify anomalies and outliers that do not reflect the main trend and are exceptions to the rules.

Here are some examples of COEX in practice:

- In the financial sector, as a measure of volatility.
- In sociological surveys - to assess public opinion.
- In the sports field, to predict/predict the winnings of teams that have objective strengths and weaknesses.

In the scientific literature, the standard deviation is denoted by the Latin letter sigma (σ), and has an alternative name - "standard deviation" (standard deviation). It is used when it is necessary to take into account all the sample values with a highly accurate result. As the name implies, the square root is required to determine the RMS.

Significance standard deviation can be put on a par with such statistical values as mean, median, mode and quartiles. One of the advantages of RMS is the ease of calculation. It is enough to carry out a few simple mathematical operations to determine the standard deviation and use it for further calculations.

Until the end of the 20th century, these operations were carried out without computers, often even without counting accessories. Today, to determine the RMS, it is enough to use software, for example, a special online application that calculates the standard deviation from the entered data.