The deviation from the actual mean of a population is known as the standard error. In statistics the standard deviation of the sampling distribution is known as the standard error.
Standard error is used to measure the standard deviation of the samples like mean or median. If the standard error is small it means that more appropriate representation of a sample is being given. Since, Standard error is inversely proportional to the sample size therefore if the sample size is larger than only standard error will be smaller.
The most common usage of the standard error is to find the mean of itself with the help of formula as stated below:
Standard error= Standard Deviation / Square Root Of the population Size
Or, it can also be found with by dividing the range of values used as a data in the standard deviation with the square root of the number. The square root size is the size of all the random samples possible.
Standard error is the approach that tells you that a population mean can be this close to the sample mean however, standard deviation measures the degree to which the individuals within a sample differs from the sample mean.
Since standard error only gives an estimate of an unknown quantity is likely to use an approach that does not involve standard error. Practically the standard deviation of the error is normally unknown, as a result of which it must be taken into account that what has been done to find the true value. Student’s t-distribution can be used to measure confidence intervals for mean or their differences instead of standard error to have more realistic values. However, standard error can be used to make an estimate of the size of the uncertainty in the confidence intervals and, its tests should be only be taken into account when the sample size is moderately large.
Standard error, as it is responsible to measure the standard deviation, therefore it is also used in the regression analysis to find the standard error of the regression. In regression analysis it as used to find the standard deviation of the underlying errors in the ordinary tests means.