Question

The size of land holdings of 380 families in a village is given below. Find the median size of land holdings.

$\begin{array}{cccccc}\text{Size of Land Holdings in(acres)}& \text{Less than 100}& 100-200& 200-300& 300-400& 400\text{and above}\\ \text{Number of Families}& 40& 89& 148& 64& 39\end{array}$

Answer 1

$\begin{array}{ccc}\text{Size of Land}& \text{Number of Families}& \text{Cumulative Frequency}\\ \text{Holdings Class Interval}& \text{(f)}& \text{(cf)}\\ 0-100& 40& 40\\ 100-200& 89& 129\\ 200-300& 148& 277\\ 300-400& 64& 341\\ 400-500& 39& 380\\ \text{Total}& \sum f=380& \end{array}$

$\sum f=N=380$

So, the median class = size of $\left(\frac{N}{2}\right)$ th item

190th item lies in the 129th cumulative frequency and the corresponding class interval is 200 - 300.

So, Median = $L+\frac{\frac{N}{2}-cf}{f}{x}_1$

$=200+\frac{190-129}{148}\times =200+\frac{61}{148}\times 100$

$=200+41.22=241.22$

Median size of land holdings = 241.22 acres.