First slide

Introduction to statistics

Question

Variance is independent of change of

Moderate

A

origin only
B

scale only
C

origin and scale both
D

none of these

Solution

If $x_{1}, x_{2}, \dots, x_{n}$ are $n$ values of a variable $X$ and $U$ is a
variable taking values $u_{1}, u_{2}, \dots, u_{n}$ such that $u_{i} = \frac{x_{i} - a}{h}$ i.e.
$x_{i} = a + h u_{i}, i = 1, 2, \dots, n .$ Then,
$Var (X) = h^{2} Var (U)$
$\Rightarrow$ Variance is independent of change of origin but not scale.

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