Question

If the standard deviation of a variable $X$ is $ \sigma , $ then the standard deviation of variable $ \frac{aX+b}{c} $ is

• A. $ a\sigma $
• B. $ \frac{a}{c}\sigma $
• C. $ \left| \frac{a}{c} \right|\sigma $
• D. $ \frac{a\sigma +b}{c} $

Answer 1

Answer: (C)

We know that, the standard deviation does not alter when a constant quantity k is added to or subtracted from each value of the variable of the series.
$ \therefore $ $ SD\left( \frac{aX+b}{c} \right)=\left| \frac{a}{c} \right|X=\left| \frac{a}{c} \right|\,\sigma (X=\sigma ) $