Tip 1: How to find sigma
Tip 1: How to find sigma
"Sigma", the letter of the Greek alphabet σ, is takencall the constant value of the root-mean-square error of the random measurement errors. The calculation of sigma is widely used in physics, statistics and related spheres of human activity. The algorithm for calculating the sigma is presented below.
You will need
- • An array of data for computing sigma;
- • Formulas for calculation;
- • Calculator or computer with Microsoft Excel software installed on it.
Instructions
1
2
3
Calculate sigma in practice. Write out the values of all measurements in one column. Calculate the arithmetic mean for all values, summing them together and dividing by the number of values.
4
From the arithmetic mean subtract each i-th value and square it. Sum all the values and divide the result by n-1 (number of values minus one).
5
The obtained value in statistics is called dispersion. We extract from it the square root. As a result, we get the standard root-mean-square error, called the sigma.
6
These calculations can be performed in standardpackage for working with Microsoft Excel spreadsheets. They can be done both in a step-by-step manner as described above, or simply by assigning the STDEV function. Check beforehand that the cell with the values has a numeric format. Be sure to specify the range of values for calculating the sigma.
Tip 2: How to find the fashion for statistics
Statistics is a function of the results of observations,with the help of which one can find an estimate of the unknown distribution parameter. For such a characteristic of a statistical distribution as a mode, the estimate is not calculated, but is selected after the primary statistical processing of the available sample. Only in individual cases and only after obtaining a theoretical distribution fashion can be found through other numerical characteristics.
Instructions
1
According to the literature data, the mode is discreterandom variable (the designation Mo) is the most probable value of it. Such a definition does not apply to continuous distributions, for them this is the value of the random variable X = Mo, at which the maximum of the probability density W (x) is reached. W (Mo) = max. Therefore, for theoretical distributions we should take the derivative of the probability density, solve the equation W '(x) = 0 and put its root equal to the mode. Some distributions do not have a mode (antimodal). The known uniform distribution is modelless. There are also multimodal cases. Mo refers to the characteristics of the position of the random variable.
2
For statistical distributions, the mode is chosenPractically the same. First of all, perform the processing of the available sample using mathematical statistics. If there was a sampling of the values of a deliberately discrete random variable, then accept the value of the mode Mo * as equal to the value that was encountered more often than others. At the same time, it is not necessary to build a polygon.
3
When processing the experimental data obtained inAs a result of observations of a continuous random variable, the entire sample is divided into separate bits and the frequencies of these bits are computed as pi * = ni / n. Here ni is the number of observations per i-th digit, and n is the sample size. In the first approximation, pi * can be considered probabilities of discrete values of a random variable. For the values themselves, use numbers corresponding to the middle of the digits. As Mo * take that number, which corresponds to the largest frequency.
4
The evaluation of the mode can be used, for example, inradiocommunications, for the development of receivers that are optimal by the criterion of the maximum a posteriori probability density. Choosing Mo * as the middle of the most probable discharge, strictly speaking, is not necessary. Just within each of the categories, the distribution is considered to be uniform. Therefore, in this case, Mo * is more of an interval rather than a point estimate, and with equal probability it can be equal to any number of the selected digit.
