The balance point is the mean of a data set. The balance point of 1, 2, 3 and 4 is (1+2+3+4)/4 = 2.5.

If you are thinking about finding the balance point of an object, it's essentially the point where the mass on the left and the right are equal. Imagine 4 balls placed at positions 1, 2, 3 and 4 on a ruler. The balance point where you can hold the ruler without it tipping either to the left or right would be 2.5.

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Let's take an example where the mass is distributed unequally like in the following picture.

There is one ball at x = 1 and 3 balls at x = 5. The balance point is at x = 4.

There are two ways to find this. First way is to find x such that the total distance of all the balls from the balance point to the right is the same as the total distance of all the balls from the balance point to the left.

We can see that the balance is at x = 4. The total distance of the three balls to the right is 3 and the total distance of the single ball to the left is 3. Therefore, this is the balance point.

The other way to find the balance point is to simply calculate the mean of the data set (1, 5, 5, 5) which is (1 + 5 + 5 + 5)/4 = 4.

Why this particular data set? The first ball is at x = 1, the second ball is at x = 5, the third ball is at x = 5 and finally the fourth ball is at x = 5.