Find the Mean and Mode of the following frequency distribution:

Class	frequency \(\displaystyle \left(f_{\mathrm{i}}\right)\)	\(\displaystyle x_{\mathrm{i}}\)	\(\displaystyle u_{\mathrm{i}=\frac{x_{i}-35}{10}}\)	\(\displaystyle f_{\mathrm{i}} u_{\mathrm{i}}\)
$\displaystyle 0$-$\displaystyle 10$	$\displaystyle 8$	$\displaystyle 5$	-$\displaystyle 3$	-$\displaystyle 24$
$\displaystyle 10$-$\displaystyle 20$	$\displaystyle 7$	$\displaystyle 15$	-$\displaystyle 2$	-$\displaystyle 14$
$\displaystyle 20$-$\displaystyle 30$	$\displaystyle 15$	$\displaystyle 25$	-$\displaystyle 1$	-$\displaystyle 15$
$\displaystyle 30$-$\displaystyle 40$	$\displaystyle 20$	\(\displaystyle 35=\mathrm{a}\)	$\displaystyle 0$	$\displaystyle 0$
$\displaystyle 40$-$\displaystyle 50$	$\displaystyle 12$	$\displaystyle 45$	$\displaystyle 1$	$\displaystyle 12$
$\displaystyle 50$-$\displaystyle 60$	$\displaystyle 8$	$\displaystyle 55$	$\displaystyle 2$	$\displaystyle 16$
$\displaystyle 60$-$\displaystyle 70$	$\displaystyle 10$	$\displaystyle 65$	$\displaystyle 3$	$\displaystyle 30$
Total	$\displaystyle 80$			$\displaystyle 5$

Modal Class is $\displaystyle 30$-$\displaystyle 40$ \[\begin{aligned} \text { Mode } & =30+\left(\frac{20-15}{2 \times 20-15-12}\right) \times 10 \\ & =\frac{440}{13} \text { or } 33.85 \text { approx. } \end{aligned} \]