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If the total number of observations is $20, \Sigma x_{i}=1000$ and
$\Sigma x_{i}^{2}=84000$, then what is the variance of the distribution?
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$\Sigma x_{i}^{2}=84000$, then what is the variance of the distribution?
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Verified Answer
The correct answer is:
1600
Total no. of observation $(n)=20$
$\Sigma x_{i}=1000$
$\bar{x}=\frac{\Sigma x_{i}}{n}=\frac{1000}{20}=50$
Variance $=s d$
$s d=\sqrt{\frac{1}{n} \Sigma x_{i}^{2}-(\bar{x})^{2}}$
$(s d)^{2}=\frac{1}{n} \Sigma x_{i}^{2}-(\bar{x})^{2}=\frac{84000}{20}-(50)^{2}$
$=4200-2500=1700$.
Variance $=1700$
$\Sigma x_{i}=1000$
$\bar{x}=\frac{\Sigma x_{i}}{n}=\frac{1000}{20}=50$
Variance $=s d$
$s d=\sqrt{\frac{1}{n} \Sigma x_{i}^{2}-(\bar{x})^{2}}$
$(s d)^{2}=\frac{1}{n} \Sigma x_{i}^{2}-(\bar{x})^{2}=\frac{84000}{20}-(50)^{2}$
$=4200-2500=1700$.
Variance $=1700$
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