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The ages of 40 students are given in the following table:

   


Find the arithmetic mean.

Solution:

    \[\begin{tabular}{|l|l|l|} \hline Age in yrs & Frequency & $\mathrm{f}_{\mathrm{i}} \mathrm{x}_{\mathrm{i}}$ \\ $\mathrm{x}_{\mathrm{i}}$ & $(\mathrm{fi})$ & \\ \hline 12 & 2 & 24 \\ \hline 13 & 4 & 52 \\ \hline 14 & 6 & 84 \\ \hline 15 & 9 & 135 \\ \hline 16 & 40 & 128 \\ \hline 17 & 7 & 119 \\ \hline 18 & 4 & 72 \\ \hline Total & 4 & 614 \\ \hline \end{tabular}\]