Standard Deviation and Standard Error (of Mean)

The terms “standard error” and “standard deviation” are often confusing.

The standard deviation (often refer as s, SD or Stddev) is a widely used measure of variability or dispersion. When we calculate the standard deviation of a sample, we are using it as an estimate of the variability of the population from which the sample was drawn.

s can be used to calculated coefficient of variation (CV)

For data with a normal distribution, about 95% of individuals will have values within 2 standard deviations of the mean, the other 5% being equally scattered above and below these limits.

The standard error of the mean (SEM or SE ) is, in statistical concept, the standard deviation of the sample mean estimate of a population mean. It can also be interpreted as the standard deviation of the error in the sample mean relative to the true mean, since the sample mean is an unbiased estimator. SEM depends on both the standard deviation and the sample size and is usually estimated by the sample estimate of the population standard deviation (sample standard deviation) divided by the square root of the sample size (assuming statistical independence of the values in the sample):