Variance

Variance - see Standard deviation.

Standard deviation is a measure of the spread of values ​​of a random variable relative to its mathematical expectation. Deviation characterizes the degree of variation of a random variable. The larger the deviation, the greater the variability of the random variable.

Deviation is usually denoted by the letter σ2 (sigma squared) and is calculated as the average of the squared deviations of individual values ​​of a random variable from its mathematical expectation.

Deviation is widely used in probability theory and mathematical statistics to characterize the dispersion of random variable values. It is often used in economics, finance, engineering calculations and other fields.

Variance - see Standard deviation.

In statistics, variance is one of the key indicators used to measure the spread of data. It allows you to estimate how distributed the values ​​in a data set are around their mean. Standard deviation and variance are closely related concepts and are often used together to analyze the spread of data.

Variance is a numerical measure of the spread of data and is calculated by measuring the difference between each value in a data set and their mean squared. The resulting differences are then summed and divided by the total number of values ​​in the data set. Thus, the formula for calculating variance is as follows:

Var(X) = Σ((Xᵢ - μ)²) / n

Where Var(X) denotes the variance, Xᵢ represents each value in the data set, μ is the mean of the data set, and n is the number of values ​​in the data set.

Deviation is a positive number and is measured in square units of the original data. A higher deviation value indicates more scatter in the data, while a lower deviation value indicates less scatter.

Deviation is often used in conjunction with standard deviation, which is the square root of the deviation. Standard deviation is a more interpretable measure of data dispersion because it has the same dimension as the original data. The formula for calculating standard deviation is as follows:

SD(X) = √Var(X)

Standard deviation is widely used in statistics and data science to analyze the distribution of data, estimate probabilities, and construct confidence intervals. It also helps identify outliers or anomalous values ​​in a data set.

In conclusion, variance is an important statistical measure used to measure the spread of data. It allows you to evaluate how much the values ​​in a data set deviate from their mean. When combined with standard deviation, standard deviation provides useful tools for analyzing data and making informed decisions in a variety of fields, including science, economics, and engineering.