Find the mean and variance for the following | vedclass

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Question

(A) The data is organized in the following table:						$x_i$			$f_i$			$f_i x_i$			$(x_i - \bar{x})^2$			$f_i(x_i - \bar{x})^2$							$92$			$3$			$27

Vedclass · Accepted Answer

Mean = $100$,Variance = $29.09$

Vedclass · Answer

(A) The data is organized in the following table:						$x_i$			$f_i$			$f_i x_i$			$(x_i - \bar{x})^2$			$f_i(x_i - \bar{x})^2$							$92$			$3$			$276$			$64$			$192$							$93$			$2$			$186$			$49$			$98$							$97$			$3$			$291$			$9$			$27$							$98$			$2$			$196$			$4$			$8$							$102$			$6$			$612$			$4$			$24$							$104$			$3$			$312$			$16$			$48$							$109$			$3$			$327$			$81$			$243$							Total			$N=22$			$\sum f_i x_i = 2200$			-			$\sum f_i(x_i - \bar{x})^2 = 640$			Here,$N = 22$ and $\sum f_i x_i = 2200$.$\bar{x} = \frac{\sum f_i x_i}{N} = \frac{2200}{22} = 100$.Variance $(\sigma^2) = \frac{1}{N} \sum f_i(x_i - \bar{x})^2 = \frac{640}{22} \approx 29.09$.

	Physics	Chemistry	Mathematics	Biology
Mean	$20$	$25$	$23$	$27$
$S$.$D$.	$3$	$2$	$4$	$5$

Find the mean and variance for the following data:

$x_i$ $92$ $93$ $97$ $98$ $102$ $104$ $109$

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

Similar Questions

The following table shows the information about marks obtained in Physics,Chemistry,Mathematics,and Biology by $100$ students in a class. Which subject shows the highest variability in marks?
Physics Chemistry Mathematics Biology
Mean $20$ $25$ $23$ $27$
$S$.$D$. $3$ $2$ $4$ $5$

The variance of the data $1, 2, 3, 5, 8, 13, 17$ is approximately

The variance of the following data is:

$x_i$ $6$ $10$ $14$ $18$ $24$ $28$ $30$

$f_i$ $2$ $4$ $7$ $12$ $8$ $4$ $3$

The variance of $50$ observations is $7$. Suppose that each observation in this data is multiplied by $6$ and then $5$ is subtracted from it. Then the variance of that new data is

The coefficient of variation of $9, 3, 11, 5, 7$ is

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$x_i$	$92$	$93$	$97$	$98$	$102$	$104$	$109$
$f_i$	$3$	$2$	$3$	$2$	$6$	$3$	$3$

Find the mean and variance for the following data: $x_i$ $92$ $93$ $97$ $98$ $102$ $104$ $109$ $f_i$ $3$ $2$ $3$ $2$ $6$ $3$ $3$