linguistic:translation
Assumptions and usage

An example of how SE {\displaystyle \operatorname {SE} } is used is to make confidence intervals of the unknown population mean. If the sampling distribution is normally distributed, the sample mean, the standard error, and the quantiles of the normal distribution can be used to calculate confidence intervals for the true population mean. The following expressions can be used to calculate the upper and lower 95% confidence limits, where x ¯ {\displaystyle {\bar {x}}} is equal to the sample mean, SE {\displaystyle \operatorname {SE} } is equal to the standard error for the sample mean, and 1.96 is the approximate value of the 97.5 percentile point of the normal distribution:

In particular, the standard error of a sample statistic (such as sample mean) is the actual or estimated standard deviation of the sample mean in the process by which it was generated. In other words, it is the actual or estimated standard deviation of the sampling distribution of the sample statistic. The notation for standard error can be any one of SE, SEM (for standard error of measurement or mean), or S.

Standard errors provide simple measures of uncertainty in a value and are often used because: