Primes in arithmetic progressions on average I

Let $E_x(q,a)$ be the error term when counting primes in arithmetic progressions and let $M(Q)={\sum }_{q\le Q}\phi (q){\sum }_{a=1}^q{E}_x(q,a{)}^3$. We show that $M(Q)<<Q^3(x\mathrm{/}Q{)}^{7\mathrm{/}5}$ for large $Q$ close to $x$ (in the usual BDH sense) thereby showing that sign changes in the error give power saving cancellation past the expected $\sqrt{x\mathrm{/}q}$ heuristic.