Multiple choice

The mean of a variable x having $50$ observations is $45$. If a new variable is defined as $U = x + 45$ the mean of the new variable is

  1. $45$
  2. $0$
  3. $95$
  4. $90$
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D Correct answer
Explanation

If every observation x is increased by 45, the mean also increases by 45. New mean = 45 + 45 = 90.

AI explanation

Using the property of means for linear transformations, if a constant value is added to every observation in a data set, that same constant is added to the mean. The original mean of the variable x is given as 45, and the new variable is defined as U equals x plus 45. Therefore, the mean of the new variable is 45 plus 45, which equals 90.

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