Standard Error Calculator

All statistics tools

Determine the precision of your sample mean compared to the population mean.

Parameters

Standard Deviation (σ)

Sample Size (n)

Error Estimation

Standard Error (SEM)1.5000

68% Confidence Interval±1.5000Mean ± 1 SEM

95% Confidence Interval±2.9400Mean ± 1.96 SEM

Standard Deviation15

Sample Size100

About this calculator

Overview

Standard Error of the Mean (SEM) measures how far the sample mean of the data is likely to be from the true population mean. It quantifies the dispersion of sample means around the true population mean. As the sample size increases, the SEM decreases, indicating a more precise estimate.

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Pro Tips

Use SEM when you want to show the precision of your estimated mean.
Ensure your sample size is at least 30 for the Central Limit Theorem to apply effectively.
If you are comparing two groups, overlapping SEM bars do not necessarily mean the difference is not significant.

Fun Facts

"In statistics, "error" does not imply a mistake but rather the natural variability inherent in sampling."
"The SEM is actually the standard deviation of the theoretical distribution of all possible sample means from a population."
"To reduce the standard error by half, you must quadruple (4x) your sample size due to the square root relationship."

Formula: SEM = σ / √n