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

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Answer 1 · 2015-12-28T22:38:27

$x=22$

$color(white)(xx)bar a =1/nsum_(i=1)^n a_i$ (the mean of a set of n data points)

$color(white)(xx)3=1/7sum_(i=1)^7 a_i$
$=>(x-4-3+1+1+2+2)/7=3$

Multiply both sides by $color(red)7$
$color(white)(xx)color(red)(7xx)(x-4-3+1+1+2+2)/7=color(red)(7xx)3$
$=>x+31=21$

Add $color(red)(+1)$ to both sides
$color(white)(xx)x-1color(red)(+1)=21color(red)(+1)$
$=>x=22$

Given the set: {2,1,-3,x,1,2,-4} {2,1,-3,x,1,2,-4} , for what x would the mean of the set be 3?