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A set of numbers will have a mean, which is defined as the sum of all the values divided by the number of values. Suppose this mean is m.
For each of the values, the squared deviation is the square of the difference between that value and m.
Algebraicly,
if you have a set {x1, x2, x3, ... , xn}, whose mean is m, then the squared deviation from the mean for x1 is (x1 - m)2.
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Can the standard deviation or variance be negative?
No, a standard deviation or variance does not have a negative sign. The reason for this is that the deviations from the mean are squared in the formula. Deviations are squared to get rid of signs. In Absolute mean deviation, sum of the deviations is taken ignoring the signs, but there is no justification for doing so. (deviations are not squared here)
1 The average of the squared deviation scores from a distribution mean?
Variance
What is the square root of the average of the squared deviations from the mean?
It is the standard deviation.
Is standard deviation the arithmetic mean of the squared deviations from the means?
No. Standard deviation is the square root of the mean of the squared deviations from the mean. Also, if the mean of the data is determined by the same process as the deviation from the mean, then you loose one degree of freedom, and the divisor in the calculation should be N-1, instead of just N.
How is standard deviation different from mean absolute decation?
If I have understood the question correctly, despite your challenging spelling, the standard deviation is the square root of the average of the squared deviations while the mean absolute deviation is the average of the deviation. One consequence of this difference is that a large deviation affects the standard deviation more than it affects the mean absolute deviation.
