Standard Error Calculator

Use the simple statistics calculator to calculate the standard error of the mean.

The Standard Error ("Std Err" or "SE"), is an indication of the reliability of the mean. A small SE is an indication that the sample mean is a more accurate reflection of the actual population mean. A larger sample size will normally result in a smaller SE (while SD is not directly affected by sample size).

STANDARD ERROR CALCULATION

How do you calculate the standard error?

• Step 1: Calculate the mean (Total of all samples divided by the number of samples).
• Step 2: Calculate each measurement's deviation from the mean (Mean minus the individual measurement).
• Step 3: Square each deviation from mean. Squared negatives become positive.
• Step 4: Sum the squared deviations (Add up the numbers from step 3).
• Step 5: Divide that sum from step 4 by one less than the sample size (n-1, that is, the number of measurements minus one)
• Step 6: Take the square root of the number in step 5. That gives you the "standard deviation (S.D.)."
• Step 7: Divide the standard deviation by the square root of the sample size (n). That gives you the "standard error".
• Step 8: Subtract the standard error from the mean and record that number. Then add the "SE" to the mean and record that number. You have plotted mean ± 1 standard error (S. E.), the distance from 1 standard error below the mean to 1 standard error above the mean