Examine the statistical error calculation

Examine the statistical error calculation

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 the 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 standard error 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.