Question

'Standard Deviation is independent of change of origin and change of scale.' Comment.

Answer 1

This statement is partially correct.

• Standard deviation is independent of the change of origin, i.e. the value of standard deviation remains the same if, in a series, a constant is added (or subtracted) to all observations.
• However, standard deviation is affected by change of scale, i.e. if all observations are multiplied or divided by a constant, then the standard deviation also gets multiplied (or divided) by this constant.