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13.Statistics
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If the variance of the following frequency distribution is $50$ then $x$ is equal to:
| Class | $10-20$ | $20-30$ | $30-40$ |
| Frequency | $2$ | $x$ | $2$ |
A
$4$
B
$-2$
C
$-4$
D
$2$
(JEE MAIN-2020)
Solution
Variance is independent of shifting of origin
$\Rightarrow y_{i}: 15 \quad 25 \quad 35 \;\; or\;\;-10 \quad 0 \quad 10$
$\Rightarrow f_{i}: 2 \quad \;\;\;x \quad \;2 \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; 2 \quad \;\;x \quad \;2$
$\Rightarrow \quad$ Variance $\left(\sigma^{2}\right)=\frac{\Sigma x _{ i }^{2} f _{ i }}{\Sigma f _{ i }}-(\overrightarrow{ x })^{2}$
$\Rightarrow \quad 50=\frac{200+0+200}{x+4}-0 \quad\{\bar{x}=0\}$
$\Rightarrow \quad 200+50 x=200+200$
$\Rightarrow \quad x=4$
Standard 11
Mathematics
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