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It is the standard deviation.

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Q: What is the square root of the average of the squared deviations from the mean?
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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)


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.


What is the sum of the squared deviations from the mean divided by the count minus one?

variation


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.


What is the square root of 8 squared?

Do you mean: What is the square root of (8 squared)? If so, there are two answers: 8 and -8. Or do you mean: What is the (square root of 8) squared? If so, there is only one answer: 8.

Related questions

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.


Why are variances squared?

The variances are squared so that all deviations above and below the mean become positive values. Taking the square root of the variance then gives a measure of the differences from the mean: the standard deviaton. Squaring the deviations also makes the bigger differences stand out. Look at 100 squared vs 10 squared.


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)


What is the standard deviation?

The standard deviation of a set of data is a measure of the spread of the observations. It is the square root of the mean squared deviations from the mean of the data.


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.


Does standard deviation and mean deviation measure dispersion the same?

No. The average of the deviations, or mean deviation, will always be zero. The standard deviation is the average squared deviation which is usually non-zero.


What is the sum of the squared deviations from the mean divided by the count minus one?

variation


The standard deviation is the square root of the average squared deviation of scores from the?

mean


Is variance based on deviations from the mean?

Variance is the squared deviation from the mean. (X bar - X data)^2


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.


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.


What is the Standard deviation of a set of data in which all the data values are the same?

ZeroDetails:The "Standard Deviation" for ungrouped data can be calculated in the following steps:all the deviations (differences) from the arithmetic mean of the set of numbers are squared;the arithmetic mean of these squares is then calculated;the square root of the mean is the standard deviationAccordingly,The arithmetic mean of set of data of equal values is the value.All the deviations will be zero and their squares will be zerosThe mean of squares is zeroThe square root of zero is zero which equals the standard deion