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

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(D) Given observations are $4, 7, 2, 8, 6, a$. The number of observations $n = 6$.The mean is given as $7$.$\frac{4 + 7 + 2 + 8 + 6 + a}{6} = 7$$\frac

Vedclass · Accepted Answer

$3$

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(D) Given observations are $4, 7, 2, 8, 6, a$. The number of observations $n = 6$.The mean is given as $7$.$\frac{4 + 7 + 2 + 8 + 6 + a}{6} = 7$$\frac{27 + a}{6} = 7$$27 + a = 42$$a = 15$.The observations are $4, 7, 2, 8, 6, 15$.Arranging in ascending order: $2, 4, 6, 7, 8, 15$.Since $n = 6$ (even),the median $M = \frac{	ext{value of } (n/2)^{th} 	ext{ term} + 	ext{value of } (n/2 + 1)^{th} 	ext{ term}}{2} = \frac{6 + 7}{2} = 6.5$.Mean deviation about median $= \frac{\sum |x_i - M|}{n}$.$x_i$$|x_i - 6.5|$$2$$4.5$$4$$2.5$$6$$0.5$$7$$0.5$$8$$1.5$$15$$8.5$Sum of deviations $= 4.5 + 2.5 + 0.5 + 0.5 + 1.5 + 8.5 = 18$.Mean deviation $= \frac{18}{6} = 3$.

Class Interval	$0-2$	$2-4$	$4-6$	$6-8$	$8-10$
Frequency	$1$	$2$	$3$	$2$	$1$

If the mean of $4, 7, 2, 8, 6$ and $a$ is $7$,find the mean deviation about the median of these observations.

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