First, expand the information.
Standard Deviation (standard deviation), a mathematical term, is the arithmetic square root of the arithmetic mean (variance) deviating from the mean square, which is expressed by σ. Standard deviation, also known as standard deviation, or experimental standard deviation, is most commonly used as the measurement basis of statistical distribution in probability statistics.
The standard deviation is the arithmetic square root of variance. The standard deviation can reflect the degree of dispersion of the data set. The standard deviation of two sets of data with the same average value may be different.
Second, the meaning of the formula
Subtract the sum of squares of all numbers, divide the result by the number of this group (or the number MINUS one, that is, the variance), and then find the root. The number is the standard deviation of this group of data.
The dark blue region is the range of values within one standard deviation of the average value. In normal distribution, the proportion of this range is 68.2% of the total value (that is, 1). For normal distribution, the ratio within two standard deviations (dark blue and blue) is 95.4%. For normal distribution, the proportion within plus or minus three standard deviations (dark blue, blue and light blue) is 99.6%.
Because of this characteristic of standard deviation, the three sigma criterion is obtained.
Three, standard deviation, standard error
Standard deviation and standard error are the contents of mathematical statistics. They are not only literally similar, but also represent the degree of dispersion from a certain standard value or intermediate value, that is, they all represent the degree of variation, but they are very different.
The standard deviation represents the degree of dispersion of sample data. The standard deviation is the square root of the variance of the sample mean. The standard deviation is usually relative to the average value of sample data, usually expressed by M SD, which indicates how far the observed value of a certain data of the sample is from the average value.
The standard error represents the sampling error. Because a population can extract countless samples, the data of each sample is an estimate of the population data. The standard deviation represents the estimation of the population data by the current sample, and the standard deviation represents the relative error between the sample mean and the population mean.