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#