To find the total number of students in the school band, we need to sum the number of students in each grade who are in the band.
From the table:
- Grade 6: 19 students
- Grade 7: 15 students
- Grade 8: 17 students
Now, we add these numbers together:
\[ 19 + 15 + 17 = 51 \]
So, the total number of students in the school band is 51.