An instructor gives students a surprise quiz and records the mean grade of $12$ points. What is the new mean value if the instructor does each of the following? Hint: for these types of problems, create a sample problem that meets these requirements. Then modify it based on each change $($presented in the bullet point$).($Privitera$,2019,$ pp$.98,$ #$22)$:

Adds $10$ points to each quiz

Subtracts $2$ points from each quiz

Doubles each quiz score

Divides each quiz score in half