Standard Error

The term standard error or standard error of the mean indicates how different the population mean is likely to be from a sample mean (Bhandari). If one is considering a complete set of experimental measurements, often called the population of measurements, then the uncertainty of the measured quantity is typically expressed in terms of the standard deviation from the mean of the measurements. But if one it taking a sample set of n independent measurements from the population, then the concept of the standard error is introduced as a strategy for estimating how well the sample represents the whole population.

When population parameters are known

When the entire reference population is known, the standard deviation of that population can be used to calculate a precise standard error.

When population parameters are unknown

When the population standard deviation is unknown, the standard deviation of the sample of measurements can be used to estimate the standard error.

Common uses of the standard error would be for sampling a large population where the total data for the population is not known. By randomly selecting a sample of values, you would be collecting data that is likely to be representative of the population. Note that increasing the sample size n, you expect to decrease the standard error by more accurately sampling the population.

If the data collected approximates a normal distribution, the standard error can be used to express the range of results in terms of confidence intervals.