Find the variance of the following data: | vedclass

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(C) Let the assumed mean be $A = 6.5$.Calculation of Variance:						$x_i$			$f_i$			$d_i = x_i - 6.5$			$f_i d_i$			$f_i d_i^2$							$3.5$			$3$			$-

Vedclass · Accepted Answer

$1.32$

Vedclass · Answer

(C) Let the assumed mean be $A = 6.5$.Calculation of Variance:						$x_i$			$f_i$			$d_i = x_i - 6.5$			$f_i d_i$			$f_i d_i^2$							$3.5$			$3$			$-3$			$-9$			$27$							$4.5$			$7$			$-2$			$-14$			$28$							$5.5$			$22$			$-1$			$-22$			$22$							$6.5$			$60$			$0$			$0$			$0$							$7.5$			$85$			$1$			$85$			$85$							$8.5$			$32$			$2$			$64$			$128$							$9.5$			$8$			$3$			$24$			$72$							Total			$N = \Sigma f_i = 217$			-			$\Sigma f_i d_i = 128$			$\Sigma f_i d_i^2 = 362$			Here,$N = 217$,$\Sigma f_i d_i = 128$,and $\Sigma f_i d_i^2 = 362$.$Var(X) = \left( \frac{1}{N} \Sigma f_i d_i^2 \right) - \left( \frac{1}{N} \Sigma f_i d_i \right)^2$$Var(X) = \frac{362}{217} - \left( \frac{128}{217} \right)^2$$Var(X) = 1.6682 - (0.5898)^2 = 1.6682 - 0.3479 = 1.3203 \approx 1.32$.

Classes	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$
Frequencies	$5$	$8$	$15$	$16$	$6$

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

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For $10$ observations $x_1, x_2, ..., x_{10}$, if $\sum_{i=1}^{10} (x_i + 2)^2 = 180$ and $\sum_{i=1}^{10} (x_i - 1)^2 = 90$, then their standard deviation is:

The variance of $10$ observations is $16$. If each observation is doubled,then the standard deviation of the new data will be -

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Find the mean and variance for the following frequency distribution.

Classes $0-10$ $10-20$ $20-30$ $30-40$ $40-50$

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If $M.D.$ is $12$,the value of $S.D.$ will be

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