The variance sigma^2 of the data is . . . . | vedclass

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

Question

$x_i$
			$f_i$
			$f_ix_i$
			$f_ix_i^2$
		
		
			$0$
			$3$
			$0$
			$0$
		
		
			$1$
			$2$
			$2$
			$2$
		
		
			$5

Vedclass · Accepted Answer

$29$

Vedclass · Answer

$x_i$
			$f_i$
			$f_ix_i$
			$f_ix_i^2$
		
		
			$0$
			$3$
			$0$
			$0$
		
		
			$1$
			$2$
			$2$
			$2$
		
		
			$5$
			$3$
			$15$
			$75$
		
		
			$6$
			$2$
			$12$
			$72$
		
		
			$10$
			$6$
			$60$
			$600$
		
		
			$12$
			$3$
			$36$
			$432$
		
		
			$17$
			$3$
			$51$
			$867$
		
		
			 
			
			$\sum f_i = 22$
			
			 
			$\sum f_ix_i^2 = 2048$
		
	


$ 	herefore \quad \sum \mathrm{f}_{\mathrm{i}} \mathrm{x}_{\mathrm{i}}=176$

$ 	ext { So } \overline{\mathrm{x}}=\frac{\sum \mathrm{f}_{\mathrm{i}} \mathrm{x}_{\mathrm{i}}}{\sum \mathrm{f}_{\mathrm{i}}}=\frac{176}{22}=8 $

$ 	ext { for } \sigma^2=\frac{1}{\mathrm{~N}} \sum \mathrm{f}_{\mathrm{i}} \mathrm{x}_{\mathrm{i}}^2-(\overline{\mathrm{x}})^2 $

$ \quad=\frac{1}{22} 	imes 2048-(8)^2$

$ \quad=93.090964 $

$\quad=29.0909$

The variance $\sigma^2$ of the data is $ . . . . . .$

$x_i$ $0$ $1$ $5$ $6$ $10$ $12$ $17$

$f_i$ $3$ $2$ $3$ $2$ $6$ $3$ $3$

Similar Questions

Let $x_1, x_2,........,x_n$ be $n$ observations such that $\sum {{x_i}^2 = 300} $ and $\sum {{x_i} = 60} $ on value of $n$ among the following is

Statement $1$ : The variance of first $n$ odd natural numbers is $\frac{{{n^2} - 1}}{3}$
Statement $2$ : The sum of first $n$ odd natural number is $n^2$ and the sum of square of first $n$ odd natural numbers is $\frac{{n\left( {4{n^2} + 1} \right)}}{3}$

The mean and standard deviation of $100$ observations were calculated as $40$ and $5.1$ , respectively by a student who took by mistake $50$ instead of $40$ for one observation. What are the correct mean and standard deviation?

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 $12$

The variance $\sigma^2$ of the data is $ . . . . . .$ $x_i$ $0$ $1$ $5$ $6$ $10$ $12$ $17$ $f_i$ $3$ $2$ $3$ $2$ $6$ $3$ $3$