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(D) The class marks $(x_i)$ are $5, 15, 25, 35, 45$ respectively.The mean is given by $\bar{x} = \frac{\sum f_i x_i}{\sum f_i} = 28$.$\frac{2(5) + 3(1

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$151$

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(D) The class marks $(x_i)$ are $5, 15, 25, 35, 45$ respectively.The mean is given by $\bar{x} = \frac{\sum f_i x_i}{\sum f_i} = 28$.$\frac{2(5) + 3(15) + x(25) + 5(35) + 4(45)}{2 + 3 + x + 5 + 4} = 28$$\frac{10 + 45 + 25x + 175 + 180}{14 + x} = 28$$\frac{410 + 25x}{14 + x} = 28$$410 + 25x = 28(14 + x)$$410 + 25x = 392 + 28x$$3x = 18 \implies x = 6$.The total frequency $N = 14 + 6 = 20$.Variance $\sigma^2 = \frac{\sum f_i x_i^2}{N} - (\bar{x})^2$.$\sum f_i x_i^2 = 2(5^2) + 3(15^2) + 6(25^2) + 5(35^2) + 4(45^2)$$= 2(25) + 3(225) + 6(625) + 5(1225) + 4(2025)$$= 50 + 675 + 3750 + 6125 + 8100 = 18700$.$\sigma^2 = \frac{18700}{20} - (28)^2 = 935 - 784 = 151$.

Class	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$
Frequency	$2$	$3$	$x$	$5$	$4$

If the mean of the frequency distribution is $28$,then its variance is $........$.

Class $0-10$ $10-20$ $20-30$ $30-40$ $40-50$

Frequency $2$ $3$ $x$ $5$ $4$

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If the mean of the frequency distribution is $28$,then its variance is $........$. Class $0-10$ $10-20$ $20-30$ $30-40$ $40-50$ Frequency $2$ $3$ $x$ $5$ $4$