Question
Let $\mu$ be the mean and $\sigma$ be the standard deviation of the distribution
| ${x_i}$ | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| ${f_i}$ | $k + 2$ | $2k$ | ${k^2} - 1$ | ${k^2} - 1$ | ${k^2} + 1$ | $k - 3$ |
where $\sum f_{i}=62$. If $[x]$ denotes the greatest integer $\leq x$, then $\left[\mu^{2}+\sigma^{2}\right]$ is equal to :