Question

If a constant is added to each value in a given data set to produce a new data set, which one of the following describes how the standard deviation of the new data compares to the standard deviation of the original data set? A. Larger B. Smaller C. Equal to

Answer 1

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.