Can you explain the standard deviation and standard error clearly?

By: ysuncn (You are welcome to reprint it. Please specify the original information)

What is standard deviation? According to the definition of the International Organization for Standardization (ISO), the standard deviation σ is the positive square root of the variance σ 2, and the variance is the expected secondary deviation of the random variable.

What is a standard error? After reading some documents, some of them are still Daniel's and their definitions are not uniform. Generally, there are two definitions:

1. The standard error of sample capacity is the standard deviation of the sample divided. PS: Here, some people use the standard deviation of the sample divided by N as the standard error (the estimation is wrong, but the standard error is based on the general mean to estimate the standard deviation, so there is no need to say wrong );
2. The standard error of a statistic can also be characterized by the standard deviation of the estimation error :.

The following is the "standard deviation and standard mistake" from the Journal edited by Hao la, which is highly relevant and I hope to help you.

The standard deviation represents a random error (or real difference) and is the statistical mean of the absolute value of a random error. In the National metering technical specifications, the standard deviation is officially named as the standard deviation, abbreviated as the standard deviation, represented by the symbol σ. There are more than 10 standard deviations, such as population standard deviation, Mother standard deviation, root mean square error, root mean square deviation, mean square error, mean square deviation, single measurement standard deviation and theoretical standard deviation. The standard deviation is defined as: The sample standard deviation s value is used as the estimated value of the general standard deviation σ. The formula for calculating the sample standard deviation is :.

In sampling tests (or repeated equi-precision measurements), standard deviations of sample mean are often used, also known as standard errors of mean or standard errors of mean ). Because the sample standard deviation s does not directly reflect the error between the sample mean X and the population mean μ, the error of the average is essentially a relative error between the sample mean and the population mean. The standard error of the available sample average is that its estimated value is, which reflects the degree of discretization of the sample average. The smaller the standard error, the closer the sample average and the general average. Otherwise, the sample average is discrete.

Standard deviation is an indicator of the variation size between individuals. It reflects the degree of discretization of the entire sample on the average sample and is a measure of data precision; the standard error reflects the variation degree of the sample average to the overall average, thus reflecting the sample error size, which is an indicator of the precision of the measurement results.

Reference: http://mathworld.wolfram.com/standarderror.html ......