Question

The standard deviation of 50 values of a variable x is 15; if each value of the variable is divided by (−3); then the standard division of the new set of 50 values of x will be
A. 15
B. -5
C. 5
D. -15

Answer 1

Hint: If a set of values with standard deviation S, are multiplied with an integer i (except zero), then the stand deviation of the new set of values will be $ S \times \left| i \right| $

Complete step-by-step answer:
We are given that the standard deviation of 50 values of a variable ‘x’ is 15.
What is the standard deviation of the 50 values of variable ‘x’ if each value of the variable ‘x’ is divided by (-3).
As we know that, multiplying a number ‘n’ with $ \dfrac{1}{a} $ is the same as dividing the same number by ‘a’.
So, here each value of the variable ‘x’ is divided by (-3) which means in other words each value of the variable ‘x’ is multiplied with $ \dfrac{1}{{ - 3}} $ .
So the standard deviation of the new set of 50 values of ‘x’ will be $ S' $
 $
  S' = S \times \left| i \right| \\
  S = 15 \\
  i = \dfrac{1}{{ - 3}} = - \dfrac{1}{3} \\
  S' = 15 \times \left| { - \dfrac{1}{3}} \right| \\
  S' = 15 \times \dfrac{1}{3} \\
  S' = 5 \\
  $
Therefore, from among the options given in question option C is correct which means the standard deviation of the new set of values of variable ‘x’ when divided by -3 will be 5.
So, the correct answer is “Option C”.

Note: Standard deviation measures the distribution of a dataset relative to its mean and is calculated as the square root of the variance and variance is the average of the squared differences of the values from the mean.