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If $\alpha, \beta$ are respectively the mean deviation about the mean and variance of the first five prime numbers, then the ordered pair $(\alpha, \beta)$
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Verified Answer
The correct answer is:
$(2.72,10.24)$
Mean of first five prime numbers
$=\frac{2+3+5+7+11}{5}=\frac{28}{5}=5.6$
$\therefore$ Mean deviation about mean
$=\frac{|2-5.6|+|3-5.6|+|5-5.6|+|7-5.6|+|11-5.6|}{5}$
$=\frac{3.6+2.6+0.6+1.4+5.4}{5}=\frac{13.6}{5}=2.72$
Variance $=\frac{\sum x i^2}{n}-\left(\frac{\sum x i}{n}\right)^2$
$=\frac{4+9+25+49+121}{5}-(5.6)^2$
$=41.6-31.36=10.24$
$=\frac{2+3+5+7+11}{5}=\frac{28}{5}=5.6$
$\therefore$ Mean deviation about mean
$=\frac{|2-5.6|+|3-5.6|+|5-5.6|+|7-5.6|+|11-5.6|}{5}$
$=\frac{3.6+2.6+0.6+1.4+5.4}{5}=\frac{13.6}{5}=2.72$
Variance $=\frac{\sum x i^2}{n}-\left(\frac{\sum x i}{n}\right)^2$
$=\frac{4+9+25+49+121}{5}-(5.6)^2$
$=41.6-31.36=10.24$
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