Question

The distributions of below give a weight of $30$ students of a class. Find the median weight of a student.

Weight (in $\mathrm{kg}$)	$40-45$	$45-50$	$50-55$	$55-60$	$60-65$	$65-70$	$70-75$
Number of students	$2$	$3$	$8$	$6$	$6$	$3$	$2$

Answer 1

Determine the median weight of a student.

Class Interval	Frequency	Cumulative frequency
$40-45$	$2$	$2$
$45-50$	$3$	$5$
$50-55$	$8$	$13$
$55-60$	$6$	$19$
$60-65$	$6$	$25$
$65-70$	$3$	$28$
$70-75$	$2$	$30$

Given parameters $\mathrm{n}=30$ and $\frac{\mathrm{n}}{2}=15$

Median class$=55-60$

$$\begin{gathered} \mathrm{l}=55 \\ {\mathrm{C}}_{\mathrm{f}}=13 \\ \mathrm{f}=6 \\ \mathrm{h}=5 \end{gathered}$$

Median $\mathbf{=}\mathit{l}\mathbf{+}\frac{\frac{\mathbf{n}}{\mathbf{2}}\mathbf{-}{\mathbf{c}}_{\mathbf{f}}}{\mathbf{f}}\mathbf{\times }\mathit{h}$

Median

$$\begin{gathered} =55+\left(\frac{(15-13)}{6}\right)\times 5 \\ =55+\left(\frac{10}{6}\right) \\ =55+1.666 \\ =56.67 \end{gathered}$$

Therefore, student's median weight is $\mathbf{56}\mathbf{.}\mathbf{67}$.