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(A) First,we calculate the mean $\bar{x} = \frac{\sum f_i x_i}{\sum f_i}$.						$x_i$			$f_i$			$f_i x_i$			$(x_i - \bar{x})^2$			$f_i(x_i - \bar{x})^

Vedclass · Accepted Answer

Variance $= 45.8$,Standard Deviation $\approx 6.77$

Vedclass · Answer

(A) First,we calculate the mean $\bar{x} = \frac{\sum f_i x_i}{\sum f_i}$.						$x_i$			$f_i$			$f_i x_i$			$(x_i - \bar{x})^2$			$f_i(x_i - \bar{x})^2$				$4$$3$$12$$100$$300$		$8$$5$$40$$36$$180$		$11$$9$$99$$9$$81$		$17$$5$$85$$9$$45$		$20$$4$$80$$36$$144$		$24$$3$$72$$100$$300$		$32$$1$$32$$324$$324$		Total$30$$420$-$1374$	Mean $\bar{x} = \frac{420}{30} = 14$.Variance $(\sigma^2) = \frac{\sum f_i(x_i - \bar{x})^2}{N} = \frac{1374}{30} = 45.8$.Standard Deviation $(\sigma) = \sqrt{45.8} \approx 6.77$.

Size $(x_i)$	$3.5$	$4.5$	$5.5$	$6.5$	$7.5$	$8.5$	$9.5$
Frequency $(f_i)$	$3$	$7$	$22$	$60$	$85$	$32$	$8$

Find the variance and standard deviation for the following data:

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

$f_i$ $3$ $5$ $9$ $5$ $4$ $3$ $1$

Similar Questions

Find the variance of the following data:

Size $(x_i)$ $3.5$ $4.5$ $5.5$ $6.5$ $7.5$ $8.5$ $9.5$

Frequency $(f_i)$ $3$ $7$ $22$ $60$ $85$ $32$ $8$

In an experiment with $15$ observations on $x$,we have $\sum x^2 = 2830$ and $\sum x = 170$. One observation that was $20$ was found to be wrong and was replaced by the correct value $30$. The corrected variance is:

The variance of the first $50$ even natural numbers is

If the standard deviation of the numbers $2, 3, a$,and $11$ is $3.5$,then which of the following is true?

Let $x_1, x_2, \dots, x_n$ be $n$ observations,$\bar{x}$ be their mean,and $\sigma^2$ be their variance.
Statement-$1$: The variance of $2x_1, 2x_2, \dots, 2x_n$ is $4\sigma^2$.
Statement-$2$: The mean of $2x_1, 2x_2, \dots, 2x_n$ is $4\bar{x}$.

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Find the variance and standard deviation for the following data: $x_i$ $4$ $8$ $11$ $17$ $20$ $24$ $32$ $f_i$ $3$ $5$ $9$ $5$ $4$ $3$ $1$