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Why to take square in the formula of standard deviation?
The sum of deviations from the mean will always be 0 and so does not provide any useful information. The absolute deviation is one solution to tat, the other is to take the square - and then take a square root.
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.
Why do you square the deviations and then turn around and find the square root of the sum of the squares?
If you simply added the deviations, their sum would always be zero. The derived statistic would not add any information. Essentially, the choice was between summing the absolute values or taking the square root of the squares. The latter has some very useful statistical properties.
How do you find the average absolute deviation?
Add all the absolute deviations together and divide by their number.
How do you calculate the sum of the deviations from the mean?
multiply the mean by the amount of numbers
What is the sum of the deviations from the mean?
The sum of standard deviations from the mean is the error.
The sum of the deviations about the mean always equals what?
The sum of total deviations about the mean is the total variance. * * * * * No it is not - that is the sum of their SQUARES. The sum of the deviations is always zero.
Why to take square in the formula of standard deviation?
The sum of deviations from the mean will always be 0 and so does not provide any useful information. The absolute deviation is one solution to tat, the other is to take the square - and then take a square root.
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)
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.
Which measure of central tendency will the sum of the deviations always be zero?
For which measure of central tendency will the sum of the deviations always be zero?
How do you find the sum of squared deviations in a set of numbers?
It would be useful to know what the deviations were from.
Definition for Sum of Absolute Deviations?
The answer depends on absolute deviation from what: the mean, median or some other measure. Suppose you have n observations, x1, x2, ... xn and you wish to calculate the sum of the absolute deviation of these observations from some fixed number c. The deviation of x1 from c is (x1 - c). The absolute deviation of x1 from c is |x1 - c|. This is the non-negative value of (x1 - c). That is, if (x1 - c) ≤ 0 then |x1 - c| = (x1 - c) while if (x1 - c) < 0 then |(x1 - c)| = - (x1 - c). Then the sum of absolute deviations is the above values, summed over x1, x2, ... xn.
Why use the squarred version of the sum of deviations from the mean?
You cannot use deviations from the mean because (by definition) their sum is zero. Absolute deviations are one way of getting around that problem and they are used. Their main drawback is that they treat deviations linearly. That is to say, one large deviation is only twice as important as two deviations that are half as big. That model may be appropriate in some cases. But in many cases, big deviations are much more serious than that a squared (not squarred) version is more appropriate. Conveniently the squared version is also a feature of many parametric statistical distributions and so the distribution of the "sum of squares" is well studied and understood.
What does the sum of the deviations from the mean equal?
Zero.
Why do you square the deviations and then turn around and find the square root of the sum of the squares?
If you simply added the deviations, their sum would always be zero. The derived statistic would not add any information. Essentially, the choice was between summing the absolute values or taking the square root of the squares. The latter has some very useful statistical properties.
How do you find the average absolute deviation?
Add all the absolute deviations together and divide by their number.
