Standard Deviation

Standard Deviation is one of the basic concepts in statistics. This is a measure of the spread of data in a sample relative to its arithmetic mean. Deviation Standard is used to evaluate the distribution of data and calculate the degree of variability of values.

In statistics, deviation is defined as the difference between each value in a sample and the arithmetic mean of the sample. Thus, the variance can be positive or negative, depending on whether each value in the sample is above or below the mean.

To calculate the Standard Deviation, you need to square each deviation, add up all the resulting squares, divide by the number of values ​​in the sample, and then take the square root of the result. The formula for calculating Standard Deviation is as follows:

SD = sqrt((1/n) * SUM((Xi - X)^2))

Where SD is Standard Deviation, n is the number of values ​​in the sample, Xi is each value in the sample, X is the arithmetic mean of the sample.

The resulting Standard Deviation value shows how much each value in the sample differs from its arithmetic mean. The larger the Standard Deviation value, the greater the spread of data in the sample.

Deviation Standard is also an important indicator for determining the significance of differences between different samples. If two samples have similar mean values ​​but have significantly different Standard Deviation, this may indicate significant differences between the samples.

In conclusion, Standard Deviation is an important measure that is used to evaluate the dispersion of data in a sample. It allows you to determine how far the values ​​in a sample differ from its arithmetic mean and is an important tool for statistical data analysis.

1. (in statistics) determination of the spread of the obtained values ​​of observed quantities near their arithmetic mean value, which is calculated as the square root of the deviations (variance) of the sample values. The arithmetic sum of all deviations from the mean must be zero; if these deviations are squared before summation, then a positive value is obtained: the average value of this value is precisely the desired standard deviation. In practice, it is more expedient to estimate the value of the standard deviation by dividing the resulting sum of squared deviations by a value that is one less than the total number of observations. See also Significance.

Introduction Standard deviation (also known as standard deviation or SD) is one of the basic statistical measures of the spread of data around the mean. This indicator is important for determining the size of a random error, which can be useful when making decisions in various fields, such as medicine,