Q: Which measure of central location will the sum of the deviation of each value from the data's average will always be zero?

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Difference (deviation) from the mean.

average is defined as a single value which has tendency to represent the data as a whole. averages are also called "measure of central tendency" or "measure of location"

They are statistical measures. For a set of observations of some random variable the mean is a measure of central tendency: a kind of measure which tells you around what value the observations are. The standard deviation is a measure of the spread around the mean.

The idea is to know how much the values "spread out" from the average.

It is a measure of how much individual values spread around the average.

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Difference (deviation) from the mean.

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.

average is defined as a single value which has tendency to represent the data as a whole. averages are also called "measure of central tendency" or "measure of location"

The mean.

the mean

It is a measure of how variable the data is. The average distance from the average.

They are statistical measures. For a set of observations of some random variable the mean is a measure of central tendency: a kind of measure which tells you around what value the observations are. The standard deviation is a measure of the spread around the mean.

The idea is to know how much the values "spread out" from the average.

It is a measure of how much individual values spread around the average.

It is a measure of the spread of the distribution: whether all the observations are clustered around a central measure or if they are spread out.

because of grace severo

mean