Deviation

A deviation is how far one data value sits from the mean, found by subtracting the mean from that value.

A deviation describes a single observation rather than the whole data set, and you write it as xixˉx_i - \bar{x}, where xˉ\bar{x} (x-bar) is the mean. A positive deviation puts the value above the mean and a negative deviation puts it below. In the data 2, 4, 6, 8 the mean is 5, so the four deviations are -3, -1, 1, and 3. They add to zero, which is true for every data set and is exactly why the variance squares the deviations before adding them up.

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