Question

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

Answer 1

`x=-56`

Explanation:

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

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

Explanation:

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`