MCQ
If the variance of the following frequency distribution :
| Class | $10-20$ | $20-30$ | $30-40$ |
| Frequency | $2$ | $x$ | $2$ |
then $x$ is equal to
- ✓$4$
- B$-2$
- C$-4$
- D$2$
| Class | $10-20$ | $20-30$ | $30-40$ |
| Frequency | $2$ | $x$ | $2$ |
then $x$ is equal to
$\Rightarrow y_{i}: 15 \quad 25 \quad 35 \;\; or\;\;-10 \quad 0 \quad 10$
$\Rightarrow f_{i}: 2 \quad \;\;\;x \quad \;2 \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; 2 \quad \;\;x \quad \;2$
$\Rightarrow \quad$ Variance $\left(\sigma^{2}\right)=\frac{\Sigma x _{ i }^{2} f _{ i }}{\Sigma f _{ i }}-(\overrightarrow{ x })^{2}$
$\Rightarrow \quad 50=\frac{200+0+200}{x+4}-0 \quad\{\bar{x}=0\}$
$\Rightarrow \quad 200+50 x=200+200$
$\Rightarrow \quad x=4$
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