Assertion (A): Adding 10 to every value of $X$ leaves its variance unchanged.
Reason (R): Adding a constant moves every value and the mean by the same amount, so the deviations from the mean stay the same.

Both A and R are true, and R is the correct explanation of A.Correct answerYour answerBoth A and R are true, but R is not the correct explanation of A.Correct answerYour answerA is true, but R is false.Correct answerYour answerA is false, but R is true.Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

$\text{Var}(X + 10) = \text{Var}(X)$ . A is true.
R says why: variance is built only from the deviations $x - \mu$ , and those do not move. R explains A.

Concept: Shifting a random variable
Typical timeTypical: 90 s
Your timeYours: —

The rule this testsVariance and standard deviation

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Ten questions from Random Variables, Expectation & Variance, at your own pace.

Assertion (A): Adding 10 to every value of XXX leaves its variance unchanged.Reason (R): Adding a constant moves every value and the mean by the same amount, so the deviations from the mean stay the same.

Explanation

Assertion (A): Adding 10 to every value of $X$ leaves its variance unchanged.
Reason (R): Adding a constant moves every value and the mean by the same amount, so the deviations from the mean stay the same.