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

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Answer 1 · 2015-11-22T10:49:47

$x = - 56$ $x=-56$

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 $n z$ $nz$ = sum of all values.

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

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

So $x + 41 = - 15$ $x+41=-15$

$x = - 15 - 41 = - 56$ $x=-15-41=-56$

Check:
$\frac{41 - 56}{5} = \frac{- 15}{5} = - 3$ $(41-56)/5 = (-15)/5 = -3$

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

Answer 2 · 2015-11-22T10:50:21

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

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

$¯ x = \frac{- 1 + 2 + (- 12) + 52 + x}{5}$ $bar(x)=(-1+2+(-12)+52+x)/5$

$¯ x = \frac{41 + x}{5}$ $bar(x)=(41+x)/5$

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

$\frac{41 + x}{5} = - 3$ $(41+x)/5=-3$

$41 + x = - 15$ $41+x=-15$

$x = - 56$ $x=-56$

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