Given a set # {-1,2,-12,52,x} #, for what x would the mean of the set be -3?

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Answer 1 · 2015-11-22T10:49:47

#x=-56#

Let the count of values be n
Let the mean be z
Let the sum be s
The mean is that single value for which #nz# = sum of all values.

So in this case the mean is -3 and n is 5. So the sum of all values is #s=zn =(-3) times 5 = -15#

The given 4 values are #(-1)+2+(-12)+52=41#

So #x+41=-15#

#x=-15-41=-56#

Check:
#(41-56)/5 = (-15)/5 = -3#

#color(green)("Confirmed that "x = -56#

Answer 2 · 2015-11-22T10:50:21

The number #x# is equal to #-56#

The mean of a set of numbers is the sum of the numbers divided by their quantity. So in this case it is:

#bar(x)=(-1+2+(-12)+52+x)/5#

#bar(x)=(41+x)/5#

According to the task the mean is #-3#, so we can write that:

#(41+x)/5=-3#

#41+x=-15#

#x=-56#