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
    $2$

Answer

Correct option: A.
$4$
a
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 $\left(\sigma^{2}\right)=\frac{\Sigma x _{ i }^{2} f _{ i }}{\Sigma f _{ i }}-(\overrightarrow{ x })^{2}$

$\Rightarrow \quad 50=\frac{200+0+200}{x+4}-0 \quad\{\bar{x}=0\}$

$\Rightarrow \quad 200+50 x=200+200$

$\Rightarrow \quad x=4$

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