Question

Calculate the median from the following data:

$\begin{array}{ccccccccc}\text{Marks (less than)}& 5& 10& 15& 20& 25& 30& 35& 40\\ \text{No. of students}& 4& 10& 20& 30& 55& 77& 95& 100\end{array}$

Answer 1

$\begin{array}{ccc}\text{Marks}& \text{No of Students(f)}& \text{C.f}\\ 0-5& 4& 4\\ 5-10& 6& 10\\ 10-15& 10& 20\\ 15-20& 10& 30\text{(C.f)}\\ \text{(L1)}20-25& 25\text{(f)}& 55\text{(Median Class)}\\ 25-30& 22& 77\\ 30-35& 18& 95\\ 35-40& 5& 100\\ & \text{N =}\sum f=100& \end{array}$

Median = $\frac{N}{2}=\frac{100}{2}=50thitem$

50th item lies in the group 20-25

$\therefore L_1=20,C.f=30,f=25,i=5$

Median = $L_1+\frac{\frac{N}{2}-C.f}{f}\times i$

$=20+\frac{50-30}{25}\times 5=24$

Median = 24 Marks