0
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.
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What will the sum of the deviation score always be?
zero
Why the standard deviation of set of data will always be greater than 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.
What does mean absolute deviation indicates?
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?
The sum of a set of data divided by the number of pieces of data is the average or mean.
I am given 9 15 28 10 and 8 what is the mean absolute deviation for this data?
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.
