An online exam is attempted by 50 candidates out of which 20 are boys. The average marks obtained by boys is 12 with a variance 2 . The variance of marks obtained by 30 girls is also 2 . The average marks of all 50 candidates is 15 . If $m$ is the average marks of girls and $\sigma^2$ is the variance of marks of 50 candidates, then $\mu+ \sigma^2$ is equal to $\_\_\_\_$ .