The problem describes a linear decrease in sputum volume, which means it follows an arithmetic progression.

The initial volume on day 1 ($a_1$) is 45 ml.
The final volume on day 7 ($a_7$) is 15 ml.
The total number of days ($n$) is 7.
We need to find the volume on the middle day.

The formula for the $n$-th term of an arithmetic progression is $a_n = a_1 + (n-1)d$.
Using $a_7 = 15$ ml and $a_1 = 45$ ml:

Subtract 45 from both sides:

Divide by 6:

The sputum volume decreases by 5 ml each day.

For a period of 7 days, the middle day is the $\frac{7+1}{2}$-th day, which is the 4-th day. So we need to find $a_4$.

Using the formula $a_n = a_1 + (n-1)d$ for $n=4$:

The middle value is the sputum volume on day 4.

The middle value is $\text{30 ml}$.