Given a set ${- 2, x, - 3, - 4, 1, 15, 22, 2}$ ${-2,x,-3,-4,1,15,22,2}$ , for what x would the mean of the set be -12?

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Given a set ${- 2, x, - 3, - 4, 1, 15, 22, 2}$ ${-2,x,-3,-4,1,15,22,2}$ , for what x would the mean of the set be -12?

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Answer 1 · 2015-12-28T18:28:52

$x = - 127$ $x=-127$

Explanation:

$\times ¯ a = \frac{1}{n} n \sum i = 1 a_{i}$ $color(white)(xx)bar a =1/nsum_(i=1)^n a_i$ (the mean of a set of n data points)

$\times - 12 = \frac{1}{8} 8 \sum i = 1 a_{i}$ $color(white)(xx)-12=1/8sum_(i=1)^8 a_i$
$\Rightarrow \frac{x - 4 - 3 - 2 + 1 + 2 + 15 + 22}{8} = - 12$ $=>(x-4-3-2+1+2+15+22)/8=-12$

Multiply both sides by $8$ $color(red)8$
$\times 8 \times \frac{x - 4 - 3 - 2 + 1 + 2 + 15 + 22}{8} = 8 \times - 12$ $color(white)(xx)color(red)(8xx)(x-4-3-2+1+2+15+22)/8=color(red)(8xx)-12$
$\Rightarrow x + 31 = - 96$ $=>x+31=-96$

Add $- 31$ $color(red)(-31)$ to both sides
$\times x + 31 - 31 = - 96 - 31$ $color(white)(xx)x+31color(red)(-31)=-96color(red)(-31)$
$\Rightarrow x = - 127$ $=>x=-127$

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Given a set ${- 2, x, - 3, - 4, 1, 15, 22, 2}$ ${-2,x,-3,-4,1,15,22,2}$ , for what x would the mean of the set be -12?

1 Answer

Explanation:

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Impact of this question

Science

Math

Humanities

... and beyond

Given a set {−2,x,−3,−4,1,15,22,2} {-2,x,-3,-4,1,15,22,2} , for what x would the mean of the set be -12?

1 Answer

Explanation:

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Impact of this question

Given a set ${- 2, x, - 3, - 4, 1, 15, 22, 2}$ ${-2,x,-3,-4,1,15,22,2}$ , for what x would the mean of the set be -12?