Standard deviation (standards deviation) and standard error You can explain that?

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What is standard deviation (deviation)? According to the International Organization for Standardization (ISO) definition: The standard deviation σ is the positive square root of the variance σ2, and the variance is the expectation of the two deviations expected by the random variable, which is not explained.

What is standard error? Read some of the literature. Some or Daniel, definitions are not uniform, usually there are two ways to define:

1, the sample size of the standard error is the standard deviation of the sample divided by. PS: Some people here use the standard deviation of the sample divided by N as the standard error (it is expected to be mistaken.) Just the standard error is based on the overall mean to predict the standard deviation , so there is no need to say that others are wrong.
2, the standard error of a statistic can also be characterized by the standard deviation of the expected error, namely:.

From the editorial journal Saradi, "standard deviation and standard error", the correlation is also larger. Hope to be of help to everyone.

As the representative of the random error (or true difference), the standard deviation is the statistical mean of the absolute value of the random error . In the National Metrology Technical Specification, the official name of the standard deviation is the standard deviations, referred to as the standard difference , denoted by the symbol σ. The name of the standard deviation has more than 10 kinds, such as the overall standard deviation, the mother standard deviation, the root mean square error, the RMS deviation, the mean square error, the mean variance, the single measurement standard deviation and the theoretical standard and so on. The standard deviation is defined as: The value of the sample standard deviation s as the estimated value of the overall standard deviation σ.

The formula for the standard deviation of the sample is:.

In the sample test (or repeated constant accuracy measurement), the standard deviation of the sample average is often used, also known as the standard error of the sample mean or the standard mistake of the abbreviation for the criterion of mean.

Because the sample standard deviation s does not directly reflect the sample mean? x and the overall average μ exactly how much error, so, the average error is essentially the average of the sample and the overall average of the relative errors. The standard of the available sample averages is mistaken, and its expected value is. It reflects the degree of dispersion of the average sample. The smaller the standard error, the closer the average of the sample to the overall average, the more discrete the mean of the sample.

The standard deviation is an indicator of the variation between individuals, which reflects the dispersion of the sample to the average of the sample, is the measure of the precision of the data , and the standard mistakenly reflects the variation of the average of the sample to the overall mean, thus reflecting the size of the sampling error, is the measurement of precision results The indicator.

Reference: Http://mathworld.wolfram.com/StandardError.html ...

Standard deviation (standards deviation) and standard error You can explain that?