The following table shows the ages of the patients admitted in a hospital during a year: Find the mode and mean of the data given above.

Age (in years)	No. of patients \(\displaystyle \left(\boldsymbol{f}_{\boldsymbol{i}}\right)\)	Mid point \(\displaystyle \left(\boldsymbol{x}_{\boldsymbol{i}}\right)\)	\(\displaystyle \boldsymbol{x}_{\boldsymbol{i}} \boldsymbol{f}_{\boldsymbol{i}}\)
$\displaystyle 5$-$\displaystyle 15$	$\displaystyle 6$	$\displaystyle 10$	$\displaystyle 60$
$\displaystyle 15$-$\displaystyle 25$	$\displaystyle 11$	$\displaystyle 20$	$\displaystyle 220$
$\displaystyle 25$-$\displaystyle 35$	$\displaystyle 21$	$\displaystyle 30$	$\displaystyle 630$
$\displaystyle 35$-$\displaystyle 45$	$\displaystyle 23$	$\displaystyle 40$	$\displaystyle 920$
$\displaystyle 45$-$\displaystyle 55$	$\displaystyle 14$	$\displaystyle 50$	$\displaystyle 700$
$\displaystyle 55$-$\displaystyle 65$	$\displaystyle 5$	$\displaystyle 60$	$\displaystyle 300$
Total	$\displaystyle 80$		$\displaystyle 2830$

\[\begin{aligned} & \begin{aligned} \Rightarrow \text { Mean } & =\frac{2830}{80} \\ & =35.375 \end{aligned} \\ & \text { Modal class }=(35-45) \\ & \begin{aligned} \Rightarrow \text { Mode } & =35+\left(\frac{23-21}{2 \times 23-21-14}\right) \times h \\ & =36.81 \end{aligned} \end{aligned} \] Therefore, mode and mean of given data are $\displaystyle 36.81$ years and $\displaystyle 35.375$ years respectively.