Question

Given a set `{-2,x,-3,-4,1,15,22,2}`, for what x would the mean of the set be -12?

Answer 1

`x=-127`

Explanation:

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

`color(white)(xx)-12=1/8sum_(i=1)^8 a_i`
`=>(x-4-3-2+1+2+15+22)/8=-12`

Multiply both sides by `color(red)8`
`color(white)(xx)color(red)(8xx)(x-4-3-2+1+2+15+22)/8=color(red)(8xx)-12`
`=>x+31=-96`

Add `color(red)(-31)` to both sides
`color(white)(xx)x+31color(red)(-31)=-96color(red)(-31)`
`=>x=-127`