If x_i is changed to x_i+a, then is changed to: - Vidyadip

MCQ

If $x_i$ is changed to $x_i+a$, then is changed to:

A
$\frac{\overline{\text{x}}}{\text{a}}$
✓
$\overline{\text{x}}-\text{a}$
C
$\overline{\text{x}}+\text{a}$
D
$\text{a}\overline{\text{x}}$

✓

Answer

Correct option: B.

$\overline{\text{x}}-\text{a}$

b. $\bar{\text{x}}-\text{a}$
Solution:
Let terms be $\text{x}_1,\text{x}_2,\text{x}_3,...,\text{x}_\text{n}$
$\therefore$ Mean ($\overline{\text{x}}$) $=\frac{\text{x}_1+\text{x}_2+\text{x}_3+..........+\text{x}_\text{n}}{\text{n}}$
New observations are $\text{x}_1+\text{a},\text{x}_2+\text{a},\text{x}_3+\text{a},...,\text{x}_\text{n}+\text{a}$
$\therefore$ New Mean $=\frac{\text{x}_1+\text{a}+\text{x}_2+\text{a}+\text{x}_3+\text{a+.........+}\text{x}_\text{n}+\text{a}}{\text{n}}$
$\frac{\text{x}_1+\text{x}_2+\text{x}_3+.......+\text{x}_\text{n}+\text{na}}{\text{n}}$
$=\overline{\text{x}}+\text{a}$

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