MCQ
$\sum(\text{x}_\text{i}-\bar{\text{x}})$ is equal to :
- ✓$0$
- B$2$
- C$1$
- D$-1$
✓
Answer
Correct option: A.
$0$
$\sum(\text{x}_\text{i}-\bar{\text{x}})=\sum(\text{x}_\text{i}-\sum(\bar{\text{x}})$
$\sum(\bar{\text{x}})=\sum(\bar{\text{n}})$ by defination
But $(\bar{\text{x}})=\frac{\sum{\text{x}_\text{i}}}{\text{n}}$ by defination
$\text{so},=\sum\text{x}_\text{i}-\sum\text{x}_\text{i}-\text{n}\frac{(\sum\text{s}_{\text{i}})}{\text{n}}$
which is equal to $=(\sum\text{x}_\text{i})-(\sum\text{x}_\text{i})=0$
$\sum(\bar{\text{x}})=\sum(\bar{\text{n}})$ by defination
But $(\bar{\text{x}})=\frac{\sum{\text{x}_\text{i}}}{\text{n}}$ by defination
$\text{so},=\sum\text{x}_\text{i}-\sum\text{x}_\text{i}-\text{n}\frac{(\sum\text{s}_{\text{i}})}{\text{n}}$
which is equal to $=(\sum\text{x}_\text{i})-(\sum\text{x}_\text{i})=0$
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