The mean and standard deviation of 15 observations were found to be 12 and 3 respectively. On rechecking it was found that an observation was read as 10 in place of 12 . If $\mu$ and $\sigma ^ { 2 }$ denote the mean and variance of the correct observations respectively, then $15 \mu + \mu ^ { 2 } + \sigma ^ { 2 }$ is equal to $\_\_\_\_$ .