Multiple choice

If both the standard deviation and mean of data set $x_1, x_2, x_3,....x_{50}$ are $16$. Then the mean of the data seg $(x_1-4)^2, (x_2-4)^2, (x_3-4)^2,.....(x_{50}-4)^2$ is?

  1. $200$
  2. $100$
  3. $400$
  4. $1600$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The mean of the transformed values is the variance plus the square of the difference between the original mean and 4. Therefore it is 16^2 + (16 - 4)^2 = 256 + 144 = 400.

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