(A) Given,

…..(i)

Now take L.H.S

So, given statement is true.

(B) Given,

Observations are = (x₁ + a), (x₂ + a), ……. (x_n + a)

⇒

From equation (i) we get,

So, given statement is true.

(C) Mean of x₁, x₂, …… x_n =

Given mean =

Observations are = ax₁, ax₂, ……..ax_n

⇒

∴ Mean = a ….. [From equation (i)]

So, the given statement is true.

(D) Let suppose the observations are =

……….( Given)

Sum = = nM…………..(i)

And

ax₁ + ax₂ + …………. + ax_n = aM

Then,

[from equation (i)]

a + M = aM (Which is not true)