When calculating the median of a frequency distribution, find the class corresponding to \( \frac{N}{2} \) and use the median formula to determine the exact value.
To find the median, we first calculate the cumulative frequency:
The total frequency \( N = 65 \). The median class corresponds to the cumulative frequency just greater than \( \frac{N}{2} = \frac{65}{2} = 32.5 \). The median class is the one with the cumulative frequency 37, which corresponds to the class interval \( 20-30 \).
Now, we use the median formula:
\[
\text{Median} = L + \left( \frac{\frac{N}{2} - F}{f} \right) \times h,
\]
where:
- \( L = 20 \) is the lower limit of the median class,
- \( F = 19 \) is the cumulative frequency of the class before the median class,
- \( f = 18 \) is the frequency of the median class,
- \( h = 10 \) is the class width.
Substituting the values:
\[
\text{Median} = 20 + \left( \frac{32.5 - 19}{18} \right) \times 10 = 20 + \left( \frac{13.5}{18} \right) \times 10 = 20 + 7.5 = 27.5.
\]
Conclusion:
The median of the given frequency distribution is \( 27.5 \).
