Question

Find the median of the following table: 

Hint:

Always find cumulative frequencies to locate the median class correctly.

Answer 1

Step 1: Find cumulative frequencies.
\[ 7, \; 15, \; 20, \; 40, \; 53, \; 60 \]
Step 2: Calculate total frequency \(N\).
\[ N = 60 \implies \frac{N}{2} = 30 \]
Step 3: Identify median class.
The class whose cumulative frequency first exceeds 30 is 30–40.
Step 4: Apply formula.
\[ \text{Median} = L + \left( \frac{\frac{N}{2} - CF}{f} \right) \times h \] Substitute values: \[ L = 30, \, CF = 20, \, f = 20, \, h = 10 \] \[ \text{Median} = 30 + \frac{(30 - 20)}{20} \times 10 = 30 + 5 = 35 \]
Step 5: Conclusion.
Hence, the median is \(\boxed{35}\).