The mean and the standard deviation (s.d.) of 10 observations are 20 and 2 respectively. Each of these 10 observations is multiplied by $p$ and then reduced by $q$, where $p \neq 0$ and $q \neq 0$. If the new mean and new s.d. become half of their original values, then $q$ is equal to $\_\_\_\_$
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