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standard deviation is the measure of the degree of dispersion. if we put the original sample on a x-y coordinate system, the second sample is basically moving every single piece of data (also including the mean of the original sample) toward positive y direction by the same amount, it does not change the degree of dispersion! thus the new stdev. does not change. if u do want to check equation, then the mean of the new sample is increased by the same amount as every other number in the sample. (Xn-mean)^2 for each item doesn't change. number of sample doesn't change, thus stdev. does not change. |