Step 1: Recall what mean means.
The mean, or average, is the total of all the values divided by how many values there are. In symbols, $\text{Mean}=\frac{\text{Sum}}{\text{Count}}$. We use this because the mean is given and one value is missing, so we can work backward.
Step 2: Count the observations.
The numbers are $5,3,0.5,4.5,a,8.5,9.5$. Counting them, there are $7$ values in all.
Step 3: Set up the equation.
Put the sum over $7$ and set it equal to the given mean $7$. \[ \frac{5+3+0.5+4.5+a+8.5+9.5}{7}=7 \]
Step 4: Add the known numbers.
Adding the known values, $5+3+0.5+4.5+8.5+9.5=31$. So the top becomes $31+a$.
Step 5: Remove the division.
Multiply both sides by $7$ to free $a$ from the fraction. \[ 31+a=49 \]
Step 6: Solve for $a$.
Subtract $31$ from both sides. \[ a=49-31=18 \] So the missing value is $18$, which is option 2. \[ \boxed{18} \]