Find the median of the following data :

We have been given data of 50 students and we need to find the median. 

Cumulative frequencies are 12 , 26, 34, 40, 50 

So, Number of observations, 𝑁 = 50

$\begin{array}{r}\Rightarrow \frac{N}{2}=\frac{50}{2}\\ \Rightarrow \frac{N}{2}=25\end{array}$

The Median class is 120 − 140

$M=I+\left[h\times \frac{\left(\frac{N}{2}-c\right)}{f}\right]$

where, 𝐼 = lower limit of median class, 𝑐 = cumulative frequency of the preceding class, 𝑓 = frequency of each class and ℎ = class size Here, 𝐼 = 120, ℎ = 20, 𝑐 = 12 , 𝑓 = 14

$\begin{array}{r}\Rightarrow M=120+\left[20\times \frac{(25-12)}{14}\right]\\ \Rightarrow M=120+\left[20\times \frac{(25-12)}{14}\right]\\ \Rightarrow M=120+\left(\frac{260}{14}\right)\\ \Rightarrow M=120+18.57\\ \Rightarrow M=138.57\end{array}$

Hence, the median is 138. 57.