Find the mean and variance for the data 6,7,1 | vedclass

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Question

$6,7,10,12,13,4,8,12$

Mean,    $\bar x = \frac{{\sum\limits_{i = 1}^8 {{x_i}} }}{n}$

$=\frac{6+7+10+12+13+4+8+12}{8}=\frac{72}{8}

Vedclass · Accepted Answer

$9.25$

Vedclass · Answer

$6,7,10,12,13,4,8,12$

Mean,    $\bar x = \frac{{\sum\limits_{i = 1}^8 {{x_i}} }}{n}$

$=\frac{6+7+10+12+13+4+8+12}{8}=\frac{72}{8}=9$

The following table is obtained


	
		
			${x_i}$
			$\left( {{x_i} - \bar x} ight)$
			${\left( {{x_i} - \bar x} ight)^2}$
		
		
			$6$
			$-3$
			$9$
		
		
			$7$
			$-2$
			$4$
		
		
			$10$
			$-1$
			$1$
		
		
			$12$
			$3$
			$9$
		
		
			$13$
			$4$
			$16$
		
		
			$4$
			$-5$
			$25$
		
		
			$8$
			$-1$
			$1$
		
		
			$12$
			$3$
			$9$
		
		
			 
			 
			$74$
		
	


Variance  $\left( {{\sigma ^2}} ight) = \frac{1}{n}\sum\limits_{i = 1}^8 {{{\left( {{x_i} - \bar x} ight)}^2} = \frac{1}{8} 	imes 74}  = 9.25$

class	0-10	10-20	20-30	30-40
Freq	1	3	4	2

Find the mean and variance for the data $6,7,10,12,13,4,8,12$

Similar Questions

Find the variance and standard deviation for the following data:

${x_i}$ $4$ $8$ $11$ $17$ $20$ $24$ $32$

${f_i}$ $3$ $5$ $9$ $5$ $4$ $3$ $1$

The mean and variance of $7$ observations are $8$ and $16$ respectively. If two observations are $6$ and $8 ,$ then the variance of the remaining $5$ observations is:

What is the standard deviation of the following series

class

0-10

10-20

20-30

30-40

Freq

1

3

4

2

The mean of the numbers $a, b, 8,5,10$ is $6$ and their variance is $6.8$. If $M$ is the mean deviation of the numbers about the mean, then $25\; M$ is equal to

${x_i}$	$\left( {{x_i} - \bar x} \right)$	${\left( {{x_i} - \bar x} \right)^2}$
$6$	$-3$	$9$
$7$	$-2$	$4$
$10$	$-1$	$1$
$12$	$3$	$9$
$13$	$4$	$16$
$4$	$-5$	$25$
$8$	$-1$	$1$
$12$	$3$	$9$
		$74$

${x_i}$	$4$	$8$	$11$	$17$	$20$	$24$	$32$
${f_i}$	$3$	$5$	$9$	$5$	$4$	$3$	$1$