Let $\bar { x } , M$ and $\sigma ^ { 2 }$ be respectively the mean, mode and variance of $n$ observations $x _ { 1 } , x _ { 2 } , \ldots , x _ { n }$ and $d _ { i } = - x _ { i } - a , i = 1,2 , \ldots , n$, where $a$ is any number. Statement I: Variance of $d _ { 1 } , d _ { 2 } , \ldots , d _ { n }$ is $\sigma ^ { 2 }$. Statement II: Mean and mode of $d _ { 1 } , d _ { 2 } , \ldots , d _ { n }$ are $- \bar { x } - a$ and $- M - a$, respectively. (1) Statement I and Statement II are both true (2) Statement I and Statement II are both false (3) Statement I is true and Statement II is false (4) Statement I is false and Statement II is true
Let $\bar { x } , M$ and $\sigma ^ { 2 }$ be respectively the mean, mode and variance of $n$ observations $x _ { 1 } , x _ { 2 } , \ldots , x _ { n }$ and $d _ { i } = - x _ { i } - a , i = 1,2 , \ldots , n$, where $a$ is any number.\\
Statement I: Variance of $d _ { 1 } , d _ { 2 } , \ldots , d _ { n }$ is $\sigma ^ { 2 }$.\\
Statement II: Mean and mode of $d _ { 1 } , d _ { 2 } , \ldots , d _ { n }$ are $- \bar { x } - a$ and $- M - a$, respectively.\\
(1) Statement I and Statement II are both true\\
(2) Statement I and Statement II are both false\\
(3) Statement I is true and Statement II is false\\
(4) Statement I is false and Statement II is true