6 The independent random variables \(X\) and \(Y\) have distributions with the same variance \(\sigma ^ { 2 }\). Random samples of \(N\) observations of \(X\) and 10 observations of \(Y\) are taken, and the results are summarised by $$\Sigma x = 5 , \quad \Sigma x ^ { 2 } = 11 , \quad \Sigma y = 10 , \quad \Sigma y ^ { 2 } = 160 .$$ These data give a pooled estimate of 12 for \(\sigma ^ { 2 }\). Find \(N\).