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(C) The first five prime numbers are $2, 3, 5, 7, 11$. Mean $(\bar{x}) = \frac{2+3+5+7+11}{5} = \frac{28}{5} = 5.6$. Mean deviation about mean $(\alph

Vedclass · Accepted Answer

$(2.72, 10.24)$

Vedclass · Answer

(C) The first five prime numbers are $2, 3, 5, 7, 11$. Mean $(\bar{x}) = \frac{2+3+5+7+11}{5} = \frac{28}{5} = 5.6$. Mean deviation about mean $(\alpha) = \frac{\sum |x_i - \bar{x}|}{n} = \frac{|2-5.6| + |3-5.6| + |5-5.6| + |7-5.6| + |11-5.6|}{5} = \frac{3.6 + 2.6 + 0.6 + 1.4 + 5.4}{5} = \frac{13.6}{5} = 2.72$. Variance $(\beta) = \frac{\sum x_i^2}{n} - (\bar{x})^2 = \frac{2^2 + 3^2 + 5^2 + 7^2 + 11^2}{5} - (5.6)^2 = \frac{4 + 9 + 25 + 49 + 121}{5} - 31.36 = \frac{208}{5} - 31.36 = 41.6 - 31.36 = 10.24$. Thus,the ordered pair $(\alpha, \beta)$ is $(2.72, 10.24)$.

Class:	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$
Freq:	$\alpha$	$110$	$54$	$30$	$\beta$

If $\alpha$ and $\beta$ are respectively the mean deviation about the mean and the variance of the first five prime numbers,then the ordered pair $(\alpha, \beta)$ is:

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