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We want to find the mean of two elements in a set, given that we know the other elements of the set and the mean of the whole set.
The answer is: -490
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For a set with N elements {x₁, x₂, ..., xₙ} the mean is given by:
Here we know that:
- The mean of the set is 0.
- The set has 1000 elements.
- 998 of these elements are ones, the other two are A and B.
We want to find the mean of the values of A and B.
First, we can start by writing the equation for the mean:
We can rewrite this as:
And we have 998 ones, then:
Now we have B isolated.
With this, the mean of A and B can be written as:
So we can conclude that the mean of the other two numbers is -490.
If you want to learn more, you can read: