Question

# 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.

Solution

## 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. Hence, New ¯X= Old ¯X×5 =40×5 =200 and, New σ= Old σ×5 =8×5 =40 (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. Hence, New ¯X= Old ¯X+7 =40+7 =47 while, New σ= Old σ =8 Economics

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