By Balance point I understand equal weight on both sides of a lever.
Various sources, including stackexchange threads use to treat 'mean' as 'balancing point'.
We want to place a fulcrum on the line so that the line doesn't tip due to the weights.
I took a simple data set to test this.
$1, 2, 3, 4, 5$
1 has less weight, 2 has more weight ...
I broken down the weights or values of each data into bar chart, like 1=1 weight 2=two 1 weights stacked on each other, so on.
Here first column = total weight 1
Second column = 1+1= total weight 2
and so on.
But it strikes shockingly, as the mean or average
$(1+2+3+4+5)/5 = 15/5 =3$ looks too off to be on the balance point.
Quite visibly, there are less blocks on the left side and more blocks on the right side. To 'balance' it, I have to choose a position that divides the blocks equally.
I have made an attempt to find the balance point, just like arranging Lego blocks.
So my questions are:
a: What I am missing here? why I am failing to process 3 (mean) as the balance point?
b: in case the balance point is really different concept from mean, then is there really a name and an application of it? Is it an existing measurement of central tendency?