First slide

Introduction to statistics

Question

If the S.D. of $x_{1}, x_{2}, \dots, x_{n}$ is 5, then the SD, of $x_{1} + 5, x_{2} + 5, x_{3} + 5, \dots, x_{n} + 5$ , is

Moderate

A

0
B

10
C

5
D

cannot say

Solution

We know that S.D. is independent of change of
origin i.e. if
$y_{i} = a x_{i} + b, i = 1, 2, \dots, n$ . Then $σ_{y} = | a | σ_{x}$
Hence, variance of $x_{1} + 5, x_{2} + 5, \dots, x_{n} + 5$ is same as the variance of $x_{1}, x_{2}, \dots, x_{n}$ i.e. $5$ .

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