The mean of a sample is:

Step 1: The formula for the mean of a grouped frequency distribution is
$\bar{x} = \frac{\sum (f_i \cdot x_i)}{N},$
where $x_i$ is the class midpoint in hours per week, $f_i$ is the frequency, and $N = 200$ students.

Step 2: Compute the class midpoints $x_i$ in hours per week.
$x_1 = \frac{0+9}{2} = 4.5,$
$x_2 = \frac{10+19}{2} = 14.5,$
$x_3 = \frac{20+29}{2} = 24.5,$
$x_4 = \frac{30+39}{2} = 34.5.$

Step 3: Compute each product $f_i \cdot x_i$ in hours per week.
$20 \times 4.5 = 90,$
$50 \times 14.5 = 725,$
$60 \times 24.5 = 1470,$
$70 \times 34.5 = 2415.$

Step 4: Sum the products.
$\sum (f_i \cdot x_i) = 90 + 725 + 1470 + 2415 = 4700.$

Step 5: Compute the mean.
$\bar{x} = \frac{4700}{200} = 23.5.$

The mean is $\boxed{23.5}$ hours per week.