The median for grouped data is given by:

$$ \text{Median} = L + \left(\frac{\frac{n}{2} - CF}{f}\right) \times h $$

where

$$L$$ is the lower limit (or boundary) of the median class.

$$CF$$ is the cumulative frequency of all classes preceding the median class.

$$f$$ is the frequency of the median class.

$$h$$ is the class width.

$$n$$ is the total number of students.

Given:

Median $$= 14$$

Median class interval is $$12-18$$, so $$L = 12$$ and the class width $$h = 18 - 12 = 6$$.

Frequency of median class $$f = 12$$.

Cumulative frequency below the median class $$= 18$$ (i.e., $$CF = 18$$).

Plugging these into the formula:

$$ 14 = 12 + \left(\frac{\frac{n}{2} - 18}{12}\right) \times 6 $$

Step 1: Subtract 12 from both sides:

$$ 2 = \left(\frac{\frac{n}{2} - 18}{12}\right) \times 6 $$

Step 2: Simplify the multiplication factor:

$$ \left(\frac{6}{12}\right) = \frac{1}{2} $$

So the equation becomes:

$$ 2 = \frac{1}{2}\left(\frac{n}{2} - 18\right) $$

Step 3: Multiply both sides by 2 to remove the fraction:

$$ 4 = \frac{n}{2} - 18 $$

Step 4: Solve for $$\frac{n}{2}$$:

$$ \frac{n}{2} = 4 + 18 = 22 $$

Step 5: Multiply both sides by 2 to find $$n$$:

$$ n = 44 $$

Thus, the total number of students is $$44$$.