# Solve clustering problem. After step 1 i.e putting each data-point to a cluster now I want to calculate the mean or average of all of the data-points in a specific cluster. let suppose we have some data-points like A(2,3), B(4,5), C(6,7), D(8,9) in a cluster. How can I calculate their average?

Solve clustering problem. After step $1$ i.e putting each data-point to a cluster now calculate the mean or average of all of the data-points in a specific cluster. let suppose We have some data-points like $A\left(2,3\right),B\left(4,5\right),C\left(6,7\right),D\left(8,9\right)$ in a cluster. How can we calculate their average?
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Note that $\left(x+y{\right)}^{3}={x}^{3}+{y}^{3}+3xy\left(x+y\right).$. If $n$ or $n+1$ is the cube of an integer, the result is clear by the uniqueness of prime factorization, so we assume that neither is the cube of an integer. Then neither is $n\left(n+1\right)$. Set $x={n}^{\frac{1}{3}}$and $y=\left(n+1{\right)}^{\frac{1}{3}}.$. If $x+y$ is rational, then so are $\left(x+y{\right)}^{3}$ and $3xy\left(x+y\right)$. Hence $3xy$ is rational. Thus $27n\left(n+1\right)$ must be the cube of an integer, a contradiction.