TS EAMCET · Maths · Statistics
Assertion (A)Variance of \(4 x_1, 4 x_2, \ldots, 4 x_n\) is 16 times the variance of \(x_1, x_2, x_3, \ldots, x_n\)Reason (R) If \(y=a x+b\), then variance of \(y\) is a (variance of \(x)+b\) The correct option among the following is
- A (A) is true, (R) is true and (R) is the correct explanation for (A).
- B (A) is true, (R) is true but \((R)\) is not the correct explanation for (A).
- C (A) is true but \((R)\) is false.
- D (A) is false but (R) is true.
Answer & Solution
Correct Answer
(C) (A) is true but \((R)\) is false.
Step-by-step Solution
Detailed explanation
Let variance of \(x_1, x_2, x_3, \ldots, x_n\) be \(\sigma^2\), then variance of \(4 x_1, 4 x_2, \ldots, 4 x_n\) is \(4^2 \sigma^2\) is \(16 \sigma^2\) And variance dependent on change of scale.
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