If the mean of 4, 7, 2, 8, 6 and a is 7,then | vedclass

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(D) Given observations are $4, 7, 2, 8, 6, a$ and the mean is $7$.We know that Mean $= \frac{4 + 7 + 2 + 8 + 6 + a}{6}$.$7 = \frac{27 + a}{6}$ $\Right

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$3$

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(D) Given observations are $4, 7, 2, 8, 6, a$ and the mean is $7$.We know that Mean $= \frac{4 + 7 + 2 + 8 + 6 + a}{6}$.$7 = \frac{27 + a}{6}$ $\Rightarrow 42 = 27 + a$ $\Rightarrow a = 15$.Now,the observations in ascending order are $2, 4, 6, 7, 8, 15$.Since the number of observations $n = 6$ (even),the median is the average of the $3^{rd}$ and $4^{th}$ observations.Median $= \frac{6 + 7}{2} = 6.5$.Mean deviation from median $= \frac{\sum |x_i - 6.5|}{6}$.$= \frac{|2 - 6.5| + |4 - 6.5| + |6 - 6.5| + |7 - 6.5| + |8 - 6.5| + |15 - 6.5|}{6}$.$= \frac{4.5 + 2.5 + 0.5 + 0.5 + 1.5 + 8.5}{6} = \frac{18}{6} = 3$.

Marks obtained	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$	$60-70$	$70-80$
No of students	$2$	$3$	$8$	$14$	$8$	$3$	$2$

If the mean of $4, 7, 2, 8, 6$ and $a$ is $7$,then the mean deviation from the median of these observations is

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