If the mean and standard deviation of 75 observations is 40 and 8 respectively, find the new mean and standard deviation if
(i) Each observation is multiplied by 5.
(ii) 7 is added to each observation.
Given: ¯X=40, σ=8, N=75
(i) A "change of scale" affects the value of both ¯X and σ. A change of scale occurs when each observation is multiplied by a constant. As a result to that, ¯X and σ also get multiplied by that constant.
In our question, that constant is 5.
New ¯X= Old ¯X×5
New σ= Old σ×5
(ii) A "change of origin" affects the value of ¯X but not that of σ. A change of origin occurs when each observation is increased by a constant. As a result to that, ¯X also increases by the same constant, while σ remains unchanged.
In our question, that constant is 7.
New ¯X= Old ¯X+7
New σ= Old σ