What is the standard deviation of the followi | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

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

Vedclass · Accepted Answer

$9$

Vedclass · Answer

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

${x_i}$	$60$	$61$	$62$	$63$	$64$	$65$	$66$	$67$	$68$
${f_i}$	$2$	$1$	$12$	$29$	$25$	$12$	$10$	$4$	$5$

What is the standard deviation of the following series

class

0-10

10-20

20-30

30-40

Freq

1

3

4

2

Similar Questions

The data is obtained in tabular form as follows.

${x_i}$ $60$ $61$ $62$ $63$ $64$ $65$ $66$ $67$ $68$

${f_i}$ $2$ $1$ $12$ $29$ $25$ $12$ $10$ $4$ $5$

If each observation of a raw data whose variance is ${\sigma ^2}$, is multiplied by $\lambda$, then the variance of the new set is

The outcome of each of $30$ items was observed; $10$ items gave an outcome $\frac{1}{2} - d$ each, $10$ items gave outcome $\frac {1}{2}$ each and the remaining $10$ items gave outcome $\frac{1}{2} + d$ each. If the variance of this outcome data is $\frac {4}{3}$ then $\left| d \right|$ equals

The mean and standard deviation of $20$ observations are found to be $10$ and $2$ respectively. On rechecking, it was found that an observation $8$ was incorrect. Calculate the correct mean and standard deviation in each of the following cases:

If it is replaced by $12$

What is the standard deviation of the following series class 0-10 10-20 20-30 30-40 Freq 1 3 4 2