Standard Deviation and Variance
The variance and the closely-related standard deviation are measures of how spread out a
distribution is. In other words, they are measures of variability.
The variance is computed as the average squared deviation of each number from its mean. For
example, for the numbers 1, 2, and 3, the mean is 2 and the variance is:
.
The formula (in summation notation) for the variance in a population is
where μ is the mean and N is the number of scores.
When the variance is computed in a sample, the statistic
(where M is the mean of the sample) can be used. S² is a biased estimate of σ², however. By far
the most common formula for computing variance in a sample is:
which gives an unbiased estimate of σ². Since samples are usually used to estimate
The variance and the closely-related standard deviation are measures of how spread out a
distribution is. In other words, they are measures of variability.
The variance is computed as the average squared deviation of each number from its mean. For
example, for the numbers 1, 2, and 3, the mean is 2 and the variance is:
.
The formula (in summation notation) for the variance in a population is
where μ is the mean and N is the number of scores.
When the variance is computed in a sample, the statistic
(where M is the mean of the sample) can be used. S² is a biased estimate of σ², however. By far
the most common formula for computing variance in a sample is:
which gives an unbiased estimate of σ². Since samples are usually used to estimate
