Question

Let $\overline{x}$, M and σ² be respectively the mean, mode and variance of n observations x₁, x₂, ...., $x_n$ and $d_{i}=x_{i}-a$, i = 1, 2, ...., n, where a is any number.
Statement I: Variance of d₁, d₂,... $d_n$ is σ².
Statement II: Mean and mode of d₁, d₂, .... $d_n$ are $-\overline{x} - a$ and – M – a, respectively.
(a) Statement I and Statement II are both false
(b) Statement I and Statement II are both true
(c) Statement I is true and Statement II is false
(d) Statement I is false and Statement II is true

Answer 1

d_{i}=x_{i}-a[/tex], i = 1, 2, ...., n, where a is any number.

Statement I: Variance of d₁, d₂,... $d_n$ is σ².

Statement II: Mean and mode of d₁, d₂, .... $d_n$ are $-\overline{x} - a$ and – M – a, respectively.

(a) Statement I and Statement II are both false

(b) Statement I and Statement II are both true

(c) Statement I is true and Statement II is false

(d) Statement I is false and Statement II is tr