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How do you calculate standard deviation?
standard deviation is the positive square root of mean of the deviations from an arithmatic mean X denoted as sigma.sigma=sqrt {(sum(x-X)^2)/n}
When computing the sample variance the sum of squared deviations about the mean is used for what reason?
You want some measure of how the observations are spread about the mean. If you used the deviations their sum would be zero which would provide no useful information. You could use absolute deviations instead. The sum of squared deviations turns out to have some useful statistical properties including a relatively simple way of calculating it. For example, the Gaussian (or Normal) distribution is completely defined by its mean and variance.
How do u calculate mean absolute deviation?
You calculate the mean.For each observation, you calculate its deviation from the mean.Convert the deviation to absolute deviation.Calculate the mean of these absolute deviations.
In any distribution is the sum of the squared deviations from the mean always equal to zero?
No. It cannot be. Remember that when you square a negative number it becomes a positive number. Thus all squared deviations are positive and their sum must be positive.
What does the sum of the deviations of each value from the mean equal?
The sum will be zero or close to zero, depending on how the sampling was done. See related question.
