Question

Find the median of the following distribution table: 

Hint:

To find the median, locate the median class using $\dfrac{n}{2}$ and apply the median formula correctly.

Answer 1

Step 1: Find cumulative frequency (CF). 

Step 2: Identify the median class. 
Total frequency \( n = 18 \). \[ \dfrac{n}{2} = 9 \] The median class is the class where cumulative frequency ≥ 9, i.e., \( 20 - 30 \). 

Step 3: Apply the formula. 
\[ \text{Median} = L + \left(\dfrac{\dfrac{n}{2} - CF_{before}}{f}\right) \times h \] Here, \( L = 20, CF_{before} = 6, f = 7, h = 10 \). \[ \text{Median} = 20 + \left(\dfrac{9 - 6}{7}\right) \times 10 = 20 + \dfrac{30}{7} = 24.3 \] 
Step 4: Conclusion. 
Hence, the median of the data is approximately 24.3.