They don't necessarily. Deviations from the median in an asymmetric data set will not sum to 0.
The mean is the sum of observations divided by the number of observations and some simple algebra will show that the sum of deviations from this equals 0. Unfortunately, the browser used by this site is useless for showing such work.
zero
The standard deviation is always be equal or higher than zero. If my set of data is limited to whole numbers, all of which are equal, the standard deviation is 0. In all other situations, we first calculate the difference of each number from the average and then calculate the square of the difference. While the difference can be a negative, the square of the difference can not be. The square of the standard deviation has to be positive, since it is the sum of all positive numbers. If we calculate s2 = 4, then s can be -2 or +2. By convention, we take the positive root.
The mean absolute deviation for a set of data is a measure of the spread of data. It is calculated as follows:Find the mean (average) value for the set of data. Call it M.For each observation, O, calculate the deviation, which is O - M.The absolute deviation is the absolute value of the deviation. If O - M is positive (or 0), the absolute value is the same. If not, it is M - O. The absolute value of O - M is written as |O - M|.Calculate the average of all the absolute deviations.One reason for using the absolute value is that the sum of the deviations will always be 0 and so will provide no useful information. The mean absolute deviation will be small for compact data sets and large for more spread out data.
The sum of a set of data divided by the number of pieces of data is the average or mean.
The mean deviation or absolute mean deviation is the sum of the differences between data values and the mean, divided by the count. In this case the MAD is 6.
It is zero.
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 sum of deviations from the mean, for any set of numbers, is always zero. For this reason it is quite useless.
Difference (deviation) from the mean.
the mean %100
zero
The standard deviation is always be equal or higher than zero. If my set of data is limited to whole numbers, all of which are equal, the standard deviation is 0. In all other situations, we first calculate the difference of each number from the average and then calculate the square of the difference. While the difference can be a negative, the square of the difference can not be. The square of the standard deviation has to be positive, since it is the sum of all positive numbers. If we calculate s2 = 4, then s can be -2 or +2. By convention, we take the positive root.
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 absolute deviation for a set of data is a measure of the spread of data. It is calculated as follows:Find the mean (average) value for the set of data. Call it M.For each observation, O, calculate the deviation, which is O - M.The absolute deviation is the absolute value of the deviation. If O - M is positive (or 0), the absolute value is the same. If not, it is M - O. The absolute value of O - M is written as |O - M|.Calculate the average of all the absolute deviations.One reason for using the absolute value is that the sum of the deviations will always be 0 and so will provide no useful information. The mean absolute deviation will be small for compact data sets and large for more spread out data.
It depends on what the deviation is from. Also, the sum of the deviations from any fixed number will always be zero.
The sum of a set of data divided by the number of pieces of data is the average or mean.
Compute & print the sum of a set of data values