During a medical checkup, height of 35 students of a class were recorded as follows: Find the difference between the mean height and median height.

Height (in cm)	Number of Students \(\displaystyle \left(f_{\mathrm{i}}\right)\)	\(\displaystyle x_{\mathrm{i}}\)	\(\displaystyle u_{\mathrm{i}=\frac{x_{i}-115}{10}}^{10}\)	\(\displaystyle f_{\mathrm{i}} u_{\mathrm{i}}\)	\(\displaystyle c f\)
$\displaystyle 90$-$\displaystyle 100$	$\displaystyle 3$	$\displaystyle 95$	-$\displaystyle 2$	-$\displaystyle 6$	$\displaystyle 3$
$\displaystyle 100$-$\displaystyle 110$	$\displaystyle 2$	$\displaystyle 105$	-$\displaystyle 1$	-$\displaystyle 2$	$\displaystyle 5$
$\displaystyle 110$-$\displaystyle 120$	$\displaystyle 4$	$\displaystyle 115$ = a	$\displaystyle 0$	$\displaystyle 0$	$\displaystyle 9$
$\displaystyle 120$-$\displaystyle 130$	$\displaystyle 5$	$\displaystyle 125$	$\displaystyle 1$	$\displaystyle 5$	$\displaystyle 14$
$\displaystyle 130$-$\displaystyle 140$	$\displaystyle 14$	$\displaystyle 135$	$\displaystyle 2$	$\displaystyle 28$	$\displaystyle 28$
$\displaystyle 140$-$\displaystyle 150$	$\displaystyle 7$	$\displaystyle 145$	$\displaystyle 3$	$\displaystyle 21$	$\displaystyle 35$
Total	$\displaystyle 35$			$\displaystyle 46$

\[\begin{aligned} \text { Mean } & =115+\frac{46}{35} \times 10 \\ & =\frac{897}{7} \text { or } 128.14 \text { approx. } \end{aligned} \] ∴ Mean height is \(\displaystyle \frac{897}{7} \mathrm{~cm}\) or $\displaystyle 128.14$ cm approx. Median Class is $\displaystyle 130$-$\displaystyle 140$ \[\begin{aligned} \text { Median } & =130+\frac{\dfrac{35}{2}-14}{14} \times 10 \\ & =132.5 \end{aligned} \] ∴ Median height is $\displaystyle 132.5$ cm Difference of mean height and median height \(\displaystyle =132.5-128.14=4.36 \mathrm{~cm}\)