# Standard Deviation Calculator

In probability theory and statistics, the standard deviation (SD) is used to describe the amount of variation in a population or sample of observations. It is defined as the distance or amount a proportion of observations in a population deviate from the population mean. It is calculated by dividing the sum of squares by the number of observations in the population. (Sum of squares)/(# of observations) = Variance. Square root of Variance = Standard deviation. The proportion of the population described by the standard deviation increases as the number of standard deviations increase. In a normally distributed population, 68% of the distribution lies within one standard deviation of the mean; 95% of the distribution lies within two standard deviations of the mean; 99.7% of the distribution lies within three standard deviations of the mean. These percentages are known as the “empirical rule”.

For example, let’s say that Americans on average will own 10 cars in their life time. And that the standard deviation is 2. The amount of cars that 68% of Americans will own will be within 1 standard deviation from the mean; in other words, 68% of Americans will own 8-12 cars in their lifetime. 95% of Americans will own 6-14 cars in their life time, and 99.7% of Americans will own 4-16 cars in their lifetime.