The Standard deviation is independent of change of(a) Origin(b) Scale(c) Both
Question
The Standard deviation is independent of change of(a) Origin(b) Scale(c) Both
Solution
The standard deviation is not independent of either change of origin or scale.
(a) Change of Origin: The standard deviation is a measure of the amount of variation or dispersion in a set of values. If you change the origin (i.e., add or subtract a constant from every value), the values will shift, but the dispersion or variation between them remains the same. Therefore, the standard deviation does not change with a change of origin.
(b) Change of Scale: However, if you change the scale (i.e., multiply or divide every value by a constant), the standard deviation will also change. This is because the standard deviation is not a relative measure, but an absolute one. It measures the absolute dispersion, not the relative dispersion. Therefore, if you multiply all values by a constant, the standard deviation will also be multiplied by the same constant.
(c) Both: Since the standard deviation is independent of the change of origin but not the change of scale, it is not independent of both.
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