defence exam Agniveer Vayu Group X & XY Mock Test 01/2026 Mathematics Statistics Variance and Standard Deviation
Let \(x_{1},x_{2},\cdots\cdot x_{n}\) be \(n\) observations, and let \(\bar{x}\) be their arithmetic mean and \(\sigma^{2}\) be their variance.
Statement 1: Variance of \(2x_{1},2x_{2},\ldots,2x_{n}\) is \(4\sigma^{2}\).
Statement 2: Arithmetic mean of \(2x_{1},2x_{2},\ldots,2x_{n}\) is \(4\bar{x}\).
1
Statement 1 is false, Statement 2 is true,
2
Statement 1 is true, Statement 2 is true, Statament 2 is a correct explanation for Statement 1
3
Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.
4
Statement 1 is true, Statement 2 is false.