If the mean of the data p, 6, 6, 7, 8, 11, 15 | vedclass

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(B) The mean of the data $p, 6, 6, 7, 8, 11, 15, 16$ is given by $\bar{x} = \frac{p + 6 + 6 + 7 + 8 + 11 + 15 + 16}{8} = \frac{p + 69}{8}$.Given that

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$3.75$

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(B) The mean of the data $p, 6, 6, 7, 8, 11, 15, 16$ is given by $\bar{x} = \frac{p + 6 + 6 + 7 + 8 + 11 + 15 + 16}{8} = \frac{p + 69}{8}$.Given that the mean is $3p$,we have $\frac{p + 69}{8} = 3p$.$p + 69 = 24p$ $\Rightarrow 23p = 69$ $\Rightarrow p = 3$.Thus,the data set is $3, 6, 6, 7, 8, 11, 15, 16$ and the mean is $\bar{x} = 3 	imes 3 = 9$.The mean deviation about the mean is given by $M.D. = \frac{1}{n} \sum_{i=1}^n |x_i - \bar{x}|$.$M.D. = \frac{|3-9| + |6-9| + |6-9| + |7-9| + |8-9| + |11-9| + |15-9| + |16-9|}{8}$.$M.D. = \frac{6 + 3 + 3 + 2 + 1 + 2 + 6 + 7}{8} = \frac{30}{8} = 3.75$.

$x_i$	$5$	$7$	$9$	$10$	$12$	$15$
$f_i$	$8$	$6$	$2$	$2$	$2$	$6$

Class interval	$0$-$10$	$10$-$20$	$20$-$30$	$30$-$40$	$40$-$50$	$50$-$60$	$60$-$70$
Frequency	$4$	$6$	$16$	$28$	$16$	$6$	$4$

If the mean of the data $p, 6, 6, 7, 8, 11, 15, 16$ is $3$ times $p$,then the mean deviation of the data from its mean is

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