What is the purpose of taking the square root of the variance to get the standard deviation?
Because of this squaring, the variance is no longer in the same unit of measurement as the original data. Taking the root of the variance means the standard deviation is restored to the original unit of measure and therefore much easier to interpret.
Which is better to use standard deviation or variance?
The SD is usually more useful to describe the variability of the data while the variance is usually much more useful mathematically. For example, the sum of uncorrelated distributions (random variables) also has a variance that is the sum of the variances of those distributions.
How is variance related to the standard error?
The relation to the properties of the actual data is quite indirect and less important. The more “fundamental” precision measure is actually the standard error, and the variance is the “reversly derived” measure relating back to the probability distribution that was constructed to describe our expectations about individual values.
Is the sum of absolute deviations a good measure of variance?
The sum of absolute deviations can be a useful metric (it provides a measure of the average “width”, which the standard formulation of variance doesn’t. However, the formulation of standard deviation provides a superior measure of average “width” for a given distribution of expected values.
How is the precision parameter related to variance?
It turned out later that the precision parameter is also related to the squared deviations. Today we often use a re-parametrization of this parameter, its reciprocal, and call it “variance”. Today it serves as a measure of the variability of the data.
How is the variance of a set of data calculated?
The variance of a set of data is obtained by calculating the mean of the squared deviations of the individual observations . Why not by taking the mean of the absolute deviations (ignoring the positive of negative signs)? There is a history how the “variance” entered statistics. There is has a paricular meaning.