Given below are two statements. Let x_ 1 , x_ 2 , x_ 3 x_ n be n observations, and let x…
Mathematics · JEE Main · NTA Exams — Statistics and Probability
Given below are two statements.
Let \(x_{1}, x_{2}, x_{3} \ldots x_{n}\) be n observations, and let \(\overline{\mathbf{x}}\) be their arithmetic mean and \(\delta^{2}\) be their variance.
STATEMENT - 1: Variance of \(2 x_{1}, 2 x_{2} \ldots 2 x_{n}\) is \(4 \delta^{2}\).
STATEMENT - 2: Arithmetic mean of \(2 x_{1}, 2 x_{2} \ldots 2 x_{n}\) is \(4 \bar{x}\).
In the light of the above statements, choose the correct answer from the options given below:
- Both the statements are true and Statement - 2 is the correct explanation for Statement - 1
- Both the statements are true but Statement - 2 is not the correct explanation for Statement - 1
- Statement - 1 is true and Statement - 2 is false
- Statement - 1 is true and Statement - 2 is false
Answer
(C) Statement - 1 is true and Statement - 2 is false
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