What is the standard deviation of the followi | vedclass

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Question

(c)


	
		
			
			$Class$
			
			$f_i$
			
			$y_i$
			
			
			$d = {y_i} - A$

			$A = 25$
			
			
			$f_id_i$
			
			
			$

Vedclass · Accepted Answer

$9$

Vedclass · Answer

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

Diameters	$33-36$	$37-40$	$41-44$	$45-48$	$49-52$
No. of circles	$15$	$17$	$21$	$22$	$25$

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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