VARIANCE AND STANDARD DEVIATION
The variance is the average squared distance from the mean. The standard deviation is the square root of the variance. The standard deviation is useful when considering how far the data are distributed from the mean.
The standard deviation represents the typical deviation of observations from the mean. Usually about 70% of the data will be within one standard deviation of the mean and about 95% will be within two standard deviations.
Like the mean, the population values for variance and standard deviation have special symbols: σ2 for the variance and σ for the standard deviation. The symbol σ is the Greek letter sigma.
Interest Rate, x = 11.57%, sx = 5.05%
6.5% 11.6% 16.7% 21.8% 26.9%
For the interest rate variable, 34 of the 50 loans (68%) had interest rates within 1 standard deviation of the mean, and 48 of the 50 loans (96%) had rates within 2 standard deviations. Usually about 70% of the data are within 1 standard deviation of the mean and 95% within 2 standard deviations, though this is far from a hard rule.
−3 −2 −1 0 1 2 3
−3 −2 −1 0 1 2 3
−3 −2 −1 0 1 2 3
Three very different population distributions with the same mean µ = 0 and standard deviation σ = 1.
