Given the set: # {1,13,-7,8,x,-2,-9,2} #, for what x would the mean of the set be 0?

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Answer 1 · 2015-12-28T18:18:29

#x=-6#

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

#color(white)(xx)0=1/8sum_(i=1)^8 a_i#
#=>(x-9-7-2+1+2+8+13)/8=0#

Multiply both sides by #color(red)8#
#color(white)(xx)color(red)(8xx)(x-9-7-2+1+2+8+13)/8=color(red)(8xx)(0)#
#=>x+6=0#

Add #color(red)(-6)# to both sides
#color(white)(xx)x+6color(red)(-6)=0color(red)(-6)#
#=>x=-6#