when a population is sampled the mean or average is generally calculated the standard error describes the variation between the calculated mean of the population and one which is considered known or accepted as accurate this helps compensate for any incidental inaccuracies related to the gathering of the sample 
the standard error of the mean refers to the standard deviation of the distribution of sample means taken from a population the relationship between the standard error and the standard deviation is such that for a given sample size the standard error equals the standard deviation divided by the square root of the sample size the deviation of the standard error is expressed as a number sometimes the deviation is necessary or desired to be shown as a percentage when shown as a percentage it is known as the relative standard error standard error and standard deviation are measures of variability while central tendency measures include mean median etc the smaller the standard error the more representative the sample will be of the overall population and the more data points involved in the calculations of the mean the smaller the standard error tends to be in cases where the standard error is large the data may have some notable irregularities in cases where multiple samples are collected the mean of each sample may vary slightly from the others creating a spread among the variables this spread is most often measured as the standard error accounting for the differences between the means across the datasets formula and calculation of standard errorused in algorithmic trading the standard error of an estimate can be calculated as the standard deviation divided by the square root of the sample size se n where the population standard deviation n the square root of the sample size begin aligned text se frac sigma surd n textbf where sigma text the population standard deviation surd n text the square root of the sample size end aligned se n where the population standard deviation n the square root of the sample size if the population standard deviation is not known you can substitute the sample standard deviation s in the numerator to approximate the standard error 1standard error vs standard deviationthe standard deviation is a representation of the spread of each of the data points it is used to help determine the validity of the data based on the number of data points displayed at each level of standard deviation standard errors function more as a way to determine the accuracy of the sample or the accuracy of multiple samples by analyzing deviation within the means the standard error normalizes the standard deviation relative to the sample size used in an analysis standard deviation measures the amount of variance or dispersion of the data spread around the mean the standard error can be thought of as the dispersion of the sample mean estimations around the true population mean example of standard errorsay that an analyst has looked at a random sample of 50 companies in the s p 500 to understand the association between a stock s p e ratio and subsequent 12 month performance in the market assume that the resulting estimate is 0 20 indicating that for every 1 0 point in the p e ratio stocks return 0 2 poorer relative performance in the sample of 50 the standard deviation was found to be 1 0 the standard error is thus therefore we would report the estimate as 0 20 0 14 giving us a confidence interval of 0 34 0 06 the true mean value of the association of the p e on returns of the s p 500 would therefore fall within that range with a high degree of probability say now that we increase the sample of stocks to 100 and find that the estimate changes slightly from 0 20 to 0 25 and the standard deviation falls to 0 90 the new standard error would thus be se 0 90 100 0 90 10 0 09 begin aligned text se frac 0 90 surd100 frac 0 90 10 0 09 end aligned se 1000 90 100 90 0 09 the resulting confidence interval becomes 0 25 0 09 0 34 0 16 which is a tighter range of values 