Standard Deviation of the Sample Mean Calculator

Your details

Use population SD when you know the true spread of the whole population. Use sample SD when you are estimating from a single sample.
The standard deviation of the entire population.
Number of observations in each sample drawn from the population.
Optional: enter a desired SEM to see what sample size you would need to achieve it with the given SD.
Standard Error of the Mean (SEM)
2.7386

Standard deviation of the sampling distribution of the mean (sigma / sqrt(n))

Variance of the Sample Mean7.5
Square root of n5.4772
2.738699.7% below · Standard deviations from the mean

SEM = 2.7386: sample means from size-30 samples will have this spread.

  • With a standard deviation of 15 and a sample size of 30, sample means will scatter around the true mean with a standard error of 2.7386.
  • Your SEM is 18.3% of the original SD. Sample means are considerably less variable than individual observations.
  • To halve the SEM to approximately 1.3693, you would need to quadruple the sample size to n = 120 (SEM would become 1.3693).
  • The variance of the sample mean is 7.5000, which equals the population variance divided by n.

Next stepSEM lets you build a 95% confidence interval for the population mean: mean +/- 1.96 x SEM (using the normal distribution when n is large).

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