Statistics and Probability: JEE Main 2023 Mathematics question

Let the mean and variance of 12 observations be $\frac{9}{2}$ and 4 respectively. Later on, it was observed that two observations were considered as 9 and 10 instead of 7 and 14 respectively. If the correct variance is $\frac{m}{n}$, where $\mathrm{m}$ and $\mathrm{n}$ are coprime, then $\mathrm{m}+\mathrm{n}$ is equal to :