Find the variance of the following discrete f | vedclass

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(D) Step $1$: Find the mid-points $(x_i)$ of each class interval: $x_1 = 1, x_2 = 3, x_3 = 5, x_4 = 7, x_5 = 9$. Step $2$: Calculate the mean $(\bar{x

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$\frac{88}{15}$

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(D) Step $1$: Find the mid-points $(x_i)$ of each class interval: $x_1 = 1, x_2 = 3, x_3 = 5, x_4 = 7, x_5 = 9$. Step $2$: Calculate the mean $(\bar{x})$: $\sum f_i = 2+3+5+3+2 = 15$. $\sum f_i x_i = (2 	imes 1) + (3 	imes 3) + (5 	imes 5) + (3 	imes 7) + (2 	imes 9) = 2 + 9 + 25 + 21 + 18 = 75$. $\bar{x} = \frac{\sum f_i x_i}{\sum f_i} = \frac{75}{15} = 5$. Step $3$: Calculate the variance $(\sigma^2)$: $\sigma^2 = \frac{\sum f_i (x_i - \bar{x})^2}{\sum f_i}$. $\sum f_i (x_i - 5)^2 = 2(1-5)^2 + 3(3-5)^2 + 5(5-5)^2 + 3(7-5)^2 + 2(9-5)^2$. $= 2(16) + 3(4) + 5(0) + 3(4) + 2(16) = 32 + 12 + 0 + 12 + 32 = 88$. $\sigma^2 = \frac{88}{15}$.

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

Find the variance of the following discrete frequency distribution:
Class Interval $0-2$ $2-4$ $4-6$ $6-8$ $8-10$
Frequency $(f_i)$ $2$ $3$ $5$ $3$ $2$

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Find the variance of the following discrete frequency distribution: Class Interval$0-2$$2-4$$4-6$$6-8$$8-10$Frequency $(f_i)$$2$$3$$5$$3$$2$