The standard deviation of the following distr | vedclass

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(A) $1$. Calculate the midpoints $(x_i)$ of each class interval: $5, 15, 25, 35$.$2$. Calculate the mean $(\bar{x})$: $\bar{x} = \frac{\sum f_i x_i}{\

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$9$

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(A) $1$. Calculate the midpoints $(x_i)$ of each class interval: $5, 15, 25, 35$.$2$. Calculate the mean $(\bar{x})$: $\bar{x} = \frac{\sum f_i x_i}{\sum f_i} = \frac{(1 	imes 5) + (3 	imes 15) + (4 	imes 25) + (2 	imes 35)}{1 + 3 + 4 + 2} = \frac{5 + 45 + 100 + 70}{10} = \frac{220}{10} = 22$.$3$. Calculate the variance $(\sigma^2)$: $\sigma^2 = \frac{\sum f_i(x_i - \bar{x})^2}{\sum f_i}$.$\sigma^2 = \frac{1(5-22)^2 + 3(15-22)^2 + 4(25-22)^2 + 2(35-22)^2}{10}$.$\sigma^2 = \frac{1(-17)^2 + 3(-7)^2 + 4(3)^2 + 2(13)^2}{10} = \frac{289 + 147 + 36 + 338}{10} = \frac{810}{10} = 81$.$4$. The standard deviation $(\sigma)$ is $\sqrt{81} = 9$.

Class interval	$0-10$	$10-20$	$20-30$	$30-40$
Frequency	$1$	$3$	$4$	$2$

Classes	$30-40$	$40-50$	$50-60$	$60-70$	$70-80$	$80-90$	$90-100$
Frequency $({f_i})$	$3$	$7$	$12$	$15$	$8$	$3$	$2$

The standard deviation of the following distribution is:
Class interval $0-10$ $10-20$ $20-30$ $30-40$
Frequency $1$ $3$ $4$ $2$

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The standard deviation of the following distribution is:Class interval$0-10$$10-20$$20-30$$30-40$Frequency$1$$3$$4$$2$