Step 1: Prepare the cumulative frequency (cf) table.
| Age | $f$ | cf |
|---|---|---|
| 15-20 | 2 | 2 |
| 20-25 | 4 | 6 |
| 25-30 | 18 | 24 |
| 30-35 | 21 | 45 |
| 35-40 | 33 | 78 |
| 40-45 | 11 | 89 |
| 45-50 | 3 | 92 |
| 50-55 | 6 | 98 |
| 55-60 | 2 | 100 |
Step 2: Total frequency $n=100$, so
$$\frac{n}{2}=\frac{100}{2}=50$$
Step 3: Locate the median class — the class whose cf first exceeds 50. Since $45<50<78$, the median class is $35-40$.
Step 4: Note the values: $l=35$, $cf=45$ (cf of class preceding the median class), $f=33$, $h=5$.
Step 5: Apply the median formula.
$$\text{Median}=l+\left(\frac{\frac{n}{2}-cf}{f}\right)\times h$$
Step 6: Substitute the values.
$$=35+\left(\frac{50-45}{33}\right)\times 5=35+\frac{25}{33}$$
Step 7: Simplify.
$$=35+0.76=35.76$$
Hence the median age of the policy holders is approximately $35.76$ years.