Let n be an odd natural number such that the variance of 1, 2, 3,...

Variance of n natural number is given by,

Variance$= \dfrac{∑ {n}^{2}}{n} - {\left(\dfrac{∑ n}{n}\right)}^{2} = \dfrac{n\left(n + 1\right)\left(2n + 1\right)}{6n} - {\left(\dfrac{n\left(n + 1\right)}{2n}\right)}^{2}$

$= \left(n + 1\right)\left[\dfrac{2n + 1}{6} - \dfrac{\left(n + 1\right)}{4}\right] = \dfrac{\left(n + 1\right)\left(n - 1\right)}{12} = \dfrac{{n}^{2} - 1}{12}$

And it is given that Variance$= 14$

$⇒ \dfrac{{n}^{2} - 1}{12} = 14$

$⇒ {n}^{2} - 1 = 168$

$⇒ n = 13$