Standard Error Calculator

Standard Error (SE) measures how much the sample mean is likely to vary from the true population mean. It indicates the precision of your sample mean as an estimate of the population mean.

Standard Error is calculated using the formula SE = s / √n, where 's' is the sample standard deviation and 'n' is the sample size. A smaller SE indicates a more precise estimate.

Standard deviation measures the spread of individual data points around the mean, while standard error measures the precision of the sample mean. SE decreases as sample size increases, but SD reflects the actual variability in your data.

Use raw data when you have the actual data points and want the calculator to compute all statistics. Use summary data when you already know the standard deviation and sample size from previous calculations.

As sample size increases, the sample mean becomes a more reliable estimate of the population mean. The SE formula divides by √n, so larger samples produce smaller standard errors and more precise estimates.

Standard Error is multiplied by a critical value (like 1.96 for 95% confidence) to create confidence intervals around the sample mean. This shows the range where the true population mean likely falls.

A small Standard Error indicates that your sample mean is likely very close to the true population mean. This suggests high precision in your measurement and that your sample size is adequate for reliable results.