Let $\rm a = \frac{11}{2}$ and $\rm b = \frac{15}{2}$.

The arithmetic mean between two numbers a and b is given by $\rm m = \frac{a + b}{2}$.

$\rm m = \frac{ \frac{11}{2} + \frac{15}{2} }{2}$

$\rm = \frac{ \frac{11 + 15}{2} }{2}$

$\rm = \frac{26}{4}$

$\rm = \frac{13}{2}$

Hence, the required arithmetic mean between the given two numbers is $\rm \frac{13}{2}$.