![]() It tells you how much the sample mean would vary if you were to repeat a study using new samples from within a single population. ![]() It is an estimate of the deviation of a sample mean from the population. The standard error of the mean, or simply standard error, indicates how different the population mean is likely to be from a sample mean. I don't know if there is an exact formula for the standard error but there is an asymptotic (in other words, approximate) one that is more complicated and more difficult to get and compute. The Standard Error of Mean, also known as SEM is another measure of variability of data. This represents how well the sample mean approximates the population mean. In other words it is the standard deviation of a large. In short: Standard Deviation is a measure of dispersion of data WITHIN a single sample which is drawn from the population under study. Calculate the standard error (of the mean). If you were using the median instead of the mean to estimate the population median (which would not be wise for Normally distributed data as the mean is a better estimator for what is ultimately the same quantity the mean and the median are equal), you would have a different standard error, a larger one. The standard error of the mean is the standard deviation of the sampling distribution of the mean. ![]() ![]() Now, imagine you measured the average height of ten random people. With reasonably large sample sizes, SD will always be the same. ![]() It tells you how much the sample mean would vary if you were to repeat a study using new samples from within a single population. If you only measured 500 people, your standard deviation would still be very close to 3.0 cm. At this point your estimate of the standard error is $\frac$, where $\sigma$ is the population standard deviation we use $s$ instead of $\sigma$ (usually presumed to be unknown) to estimate the standard error. What is standard error The standard error of the mean, or simply standard error, indicates how different the population mean is likely to be from a sample mean. ![]()
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