Question

Find the median of the following frequency distribution: 

Hint:

Always find the class where the cumulative frequency just exceeds \( \frac{N}{2} \); this is the median class. Use the formula \( \text{Median} = l + \left( \frac{\frac{N}{2} - c}{f} \right) h \).

Answer 1

Step 1: Find the cumulative frequency (cf). 

Step 2: Identify the median class. 
Total frequency \( N = 60 \). \[ \frac{N}{2} = 30 \] The cumulative frequency just greater than 30 is 33, corresponding to the class interval 20–30. Hence, the median class is \( 20 - 30 \). 
Step 3: Write the median formula. 
\[ \text{Median} = l + \left(\frac{\frac{N}{2} - c}{f}\right) \times h \] where \( l = \) lower boundary of median class = 20 
\( c = \) cumulative frequency before median class = 13 
\( f = \) frequency of median class = 20 
\( h = \) class size = 10 
\( N = 60 \) 
Step 4: Substitute the values. 
\[ \text{Median} = 20 + \left(\frac{30 - 13}{20}\right) \times 10 \] \[ \text{Median} = 20 + \left(\frac{17}{20}\right) \times 10 \] \[ \text{Median} = 20 + 8.5 = 28.5 \] Step 5: Final Answer. 
\[ \boxed{\text{Median} = 28.5} \]