Given a set {12, x ,17} {12,x,17}, for what x would the mean be 14?

1 Answer
Özgür Özer
Dec 7, 2015

x=13x=13

Explanation:

color(white)(xx)bar a =1/nsum_(i=1)^n a_iׯa=1nn∑i=1ai (the mean of a set of n data points)

color(white)(xx)14=1/3sum_(i=1)^3 a_i×14=133∑i=1ai
=>(12+x+17)/3=14⇒12+x+173=14

Multiply both sides by 33
color(white)(xx)color(red)(3*)(12+x+17)/3=color(red)(3*)14×3⋅12+x+173=3⋅14
=>x+29=42⇒x+29=42

Add -29−29 to both sides
color(white)(xx)x+29color(red)(-29)=42color(red)(-29)×x+29−29=42−29
=>x=13⇒x=13

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