Question

Find the median from the following frequency distribution: 

Hint:

For the median in a frequency table, always find the class where cumulative frequency first exceeds $N/2$.

Answer 1

Step 1: Compute cumulative frequencies. 

Step 2: Find $N/2$. 
\[ N = 59, \quad N/2 = 29.5 \] Step 3: Locate the median class. 
The class with cumulative frequency just greater than 29.5 is 20–30. 
Step 4: Apply the median formula. 
\[ \text{Median} = L + \left(\dfrac{\dfrac{N}{2} - CF}{f}\right) \times h \] Substitute: $L = 20, \, CF = 15, \, f = 20, \, h = 10$ \[ \text{Median} = 20 + \left(\dfrac{29.5 - 15}{20}\right) \times 10 = 20 + 7.25 = 27.25 \] Step 5: Conclusion. 
Hence, the median = 27.25.