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Size analysis was carried out on a sample of gravel. The data for mass fraction $(x_{i})$ and average particle diameter $(D_{pi})$ of the fraction is given in the table below:

$$\begin{array}{clcI|cI|cI|cI|c}\hline
&\textbf{x$_{i}$} & \textbf{D$_{pi}$ (mm)} \\ \hline &\text{0.2} & \text{5} \\ &\text{0.4} & \text{10} \\ &\text{0.4} &\text{20}\\ \hline \end{array}$$

The mass mean diameter of the sample, to the nearest integer, is _____________ $mm$.
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