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Why take the square root of the variance when calculation standard deviation?
The variance is based on the squares of the variable being studied. If, for example, the variable is mass, then the variance is measured in mass-squared. Most people will not be able to wrap their heads around the square of mass. However, the square root will be in the same units of measurement as the variable itself. Thus, the idea of a variable being distributed about a mean, M (also measured in the same units), with a standard deviation (or error) of S is easier to understand.Second, under reasonable conditions,the transformed variable obtained by subtracting the mean and dividing the result by the standard deviation will have a standard normal distribution. This is extremely important for estimation and hypothesis testing.
What is a difference between a pooled variance and a combined variance?
Pooled variance is a method for estimating variance given several different samples taken in different circumstances where the mean may vary between samples but the true variance (equivalently, precision) is assumed to remain the same. A combined variance is a method for estimating variance from several samples, given the size, mean and standard deviation of each. Mathematically, a combined variance is equal to the calculated variance of the set of the data from all samples. See links.
How do you calculate mean average deviation?
The mean average deviation is the same as the mean deviation (or the average deviation) and they are, by definition, 0.
Is the standard deviation the same as the mean of absolute distances from the mean?
no the standard deviation is not equal to mean of absolute distance from the mean
What does homogeneity of variance mean?
It means that the variance remains the same across the range of values of the variable.
