Standard Error of the Mean

Standard error of the mean

Tells you how accurate your estimate of the mean is likely to be. Calculated by the standard deviation of the observations divided by the square root of the sample size.

Single sample of observations

You can estimate the standard error of the mean using the sample size and standard deviation of a single sample of observations.

If you take many random samples

The standard error of the mean is the standard deviation of the different sample means. 2/3 of the sample means would be within 1 standard error. 95.4% would be within 2 standard errors. 99.7% would be within 3 standard errors.

Effect of sample size

If small sample size = estimate of the mean won't be as good as an estimate based on a larger sample size. As you increase your sample size, the standard error of the mean will become smaller.

Parametric mean

When you take a sample of observations from a population and calculate the sample mean, you are estimating the mean of all the individuals in the population