A. Imagine that the list of numbers turns out to be too low by 5. That 5 should

Question

A.   Imagine that the list of numbers turns out to be too low by 5. That 5 should be added to each number. In each of the following, you may do the math, but you do not need to in order to get full credit. How will the average change?
   A.   It will be smaller
   B. It will remain the same
   C. It will be larger
   D.    Cannot be determined with the information given

B.   Imagine that the list of numbers turns out to be too low by 5. That 5 should be added to each number. In each of the following, you may do the math, but you do not need to in order to get full credit. How will the standard deviation change?
   A.     It will be smaller
   B.     It will remain the same
   C.     It will be larger
   D.     Cannot be determined with the information given

Explanation / Answer

Let there are n numbers

Let their average be m

So their sum is mn

If each no is increased by 5

New sum will be mn+5n

New mean is m+5

So option C is correct

Average will be larger

B)

Standard deviation is invariant to the change of location.

So

Option B is correct.

Standard deviation will remain same.

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