Answer
The total linear momentum of this group is 0 at any given instant.
Work Step by Step
Momentum is a vector and can be found using this formula: $$\vec{p}=m\vec{v}$$
The people standing still already have zero momentum.
For the people walking around, if we take a person A with mass $m_A$ and velocity $\vec{v_A}$, it is very likely that there is a person $B$ with mass $m_B=m_A$ and velocity $\vec{v_B}=-\vec{v_A}$. These two make $\vec{p_A}+\vec{p_B}=0$
Continue thinking like that and we end up finding that the total linear momentum of this group is 0 at any given instant.
