Question

Find the median of the following data:

Weight (in 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

We prepare the cumulative frequency table, as given below:

$\frac{N}{2}=\frac{30}{2}=15$
Cumulative frequency just greater than 15 is 19.
Corresponding class interval is 55 - 60.
Thus, median class is 55 - 60.
Cumulative frequency just before this class = 13
So, l = 55, f = 6 , $\frac{N}{2}=15$, h = 5 and cf = 13
$\mathrm{Median},M_e=l+\left\{h\times \frac{\left({\displaystyle \frac{N}{2}}-cf\right)}{f}\right\}$
$$\begin{gathered} =55+\left\{5\times \left(\frac{15-13}{6}\right)\right\} \\ =55+\frac{5\times 2}{6} \\ =55+1.67 \\ =56.67 \end{gathered}$$
Hence, median = 56.67 kg