Answer: C. Equal to
Step-by-step explanation:
The standard deviation is written as:
Sx = √( ∑(xₙ - x)^2/(n-1))
Where xₙ are the values of the data set, n is the number of data points and x is the mean of the data set.
Now, if we add a constant c to all the terms in our data set we will have:
(i will use the ' to denote the transformed data)
xₙ' are now xₙ + c.
And the new mean will be:
x' = ( (x₁ + c) + (x₂ + c) + .... + (xₙ + c))/n = (c*n + (x₁ + x₂ + ..))/n = c + (x₁ + x₂ +...)/n
x' = c + x
Then the new standard deviation will be:
Sx' =√( ∑(xₙ' - x')^2/(n-1))
Sx' = √( ∑((xₙ+c) - (x +c))^2/(n-1)) = √( ∑(xₙ - x)^2/(n-1)) = Sx
So the standard deviation does not change.
The correct option is C.
