What is the standard deviation of the followi | vedclass

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Question

Class
			$f$
			${y_i}$
			
			$d = {y_i} - A,$

			$A = 25$
			
			${f_i}{d_i}$
			${f_i}d_i^2$
		
		
			$0-10$
			$1$
			$

Vedclass · Accepted Answer

$9$

Vedclass · Answer

Class
			$f$
			${y_i}$
			
			$d = {y_i} - A,$

			$A = 25$
			
			${f_i}{d_i}$
			${f_i}d_i^2$
		
		
			$0-10$
			$1$
			$5$
			$-20$
			$-20$
			$400$
		
		
			$10-20$
			$3$
			$15$
			$-10$
			$-30$
			$300$
		
		
			$20-30$
			$4$
			$25$
			$0$
			$0$
			$0$
		
		
			$30-40$
			$2$
			$35$
			$10$
			$20$
			$200$
		
		
			Total
			$10$
			 
			 
			$-30$
			$900$
		
	


${\sigma ^2} = \frac{{\sum {{f_i}} d_i^2}}{{\sum {{f_i}} }} - {\left( {\frac{{\sum {{f_i}} {d_i}}}{{\sum {{f_i}} }}} \right)^2}$

$=\frac{900}{10}-\left(\frac{-30}{10}\right)^{2}$

$\sigma^{2}=90-9=81 $

$\Rightarrow \sigma=9$

Height in cms	$70-75$	$75-80$	$80-85$	$85-90$	$90-95$	$95-100$	$100-105$	$105-110$	$110-115$
No. of children	$3$	$4$	$7$	$7$	$15$	$9$	$6$	$6$	$3$

$X_i$	$0$	$1$	$2$	$3$	$4$	$5$
$f_i$	$k+2$	$2k$	$K^{2}-1$	$K^{2}-1$	$K^{2}-1$	$k-3$

What is the standard deviation of the following series

class $0-10$ $10-20$ $20-30$ $30-40$

Freq $1$ $3$ $4$ $2$

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