Standard Error of the Mean

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Example: the weight of a coffee bag varies with a standard deviation of 12 g. Weighing 36 bags and taking the mean, how far off does that mean usually land? Change the values to work out your own case.

Standard deviation σ Sample size n

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What each term means

Standard Error (SE): The standard deviation of the sample mean: how much the mean of n values varies from one sample to the next. It is the piece that goes into confidence intervals and tests for the mean.
Standard Deviation (σ): How much each individual value varies around the population mean. When σ is unknown, the sample standard deviation s is used.
Square Root of the Sample Size (√n): Means of more values vary less, because deviations up and down offset each other. But the gain goes by the root: halving the error takes four times as much data.