Given a set # {-15,1,200,x,1} #, for what x would the mean of the set be -15?

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Answer 1 · 2015-12-11T08:41:40

#color(white)(xx)-262#

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

#color(white)(xx)-15=1/5sum_(i=1)^5 a_i#
#=>(-15+1+200+x+1)/5=-15#

Multiply both sides by #5#
#color(white)(xx)color(red)(5*)(-15+1+200+x+1)/5=color(red)(5*)(-15)#
#=>x+187=-75#

Add #-187# to both sides
#color(white)(xx)x+187color(red)(-187)=-75color(red)(-187)#
#=>x=-262#