The sum of deviations from the mean, for any set of numbers, is always zero. For this reason it is quite useless.
Variance is standard deviation squared. If standard deviation can be zero then the variance can obviously be zero because zero squared is still zero. The standard deviation is equal to the sum of the squares of each data point in your data set minus the mean, all that over n. The idea is that if all of your data points are the same then the mean will be the same as every data point. If the mean is the equal to every data point then the square of each point minus the mean would be zero. All of the squared values added up would still be zero. And zero divided by n is still zero. In this case the standard deviation would be zero. Short story short: if all of the points in a data set are equal than the variance will be zero. Yes the variance can be zero.
The mean absolute deviation for one number is always zero.
What is mean deviation and why is quartile deviation better than mean deviation?
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)
It is zero.
The sum of deviations from the mean, for any set of numbers, is always zero. For this reason it is quite useless.
zero
Difference (deviation) from the mean.
the mean %100
if no absolute value is used the sum is zero.
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.
The deviation about the mean of a single number is always zero.
You don't need to. The mean deviation is, by definition, zero.
The sum of the differences between each score and the mean is always zero. This is because the mean is the "center" of the data and any deviation from the mean in one direction is offset by an equal deviation in the opposite direction. This property is essential in understanding the concept of the mean as a measure of central tendency.
The mean deviation of any set of numbers is always zero and so the absolute mean deviation is also always zero.
The total deviation from the mean for ANY distribution is always zero.