If the standard deviation of a variable X is σ , then the standard deviation of variable (aX+b/c) is

Question

If the standard deviation of a variable X is σ , then the standard deviation of variable (aX+b/c) is (A)  aσ  (B)  (a/c)σ  (C)  | (a/c) |σ  (D)  (aσ +b/c)

Tardigrade Admin · Accepted Answer

We know that, the standard deviation does not alter when a constant quantity k is added to or subtracted from each value of the variable of the series.

∴

S D (\frac{a X + b}{c}) = ∣ ∣ \frac{a}{c} ∣ ∣ X = ∣ ∣ \frac{a}{c} ∣ ∣ σ (X = σ)

Q. If the standard deviation of a variable $X$ is $σ,$ then the standard deviation of variable $\frac{a X + b}{c}$ is

$aσ$

$\frac{a}{c} σ$

$∣ ∣ \frac{a}{c} ∣ ∣ σ$

$\frac{aσ + b}{c}$

We know that, the standard deviation does not alter when a constant quantity k is added to or subtracted from each value of the variable of the series.
$∴$ $S D (\frac{a X + b}{c}) = ∣ ∣ \frac{a}{c} ∣ ∣ X = ∣ ∣ \frac{a}{c} ∣ ∣ σ (X = σ)$

Q. If the standard deviation of a variable X is σ, then the standard deviation of variable caX+b​ is

aσ

ca​σ

∣∣​ca​∣∣​σ

caσ+b​