Question

Find the median of the following frequency distribution:

Hint:

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.

Answer 1

To find the median, we first calculate the cumulative frequency:

The total frequency \( N = 55 \). The median class corresponds to the cumulative frequency just greater than or equal to \( \frac{N}{2} = \frac{55}{2} = 27.5 \). The cumulative frequency just greater than 27.5 is 33, 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, - \( F = 13 \) is the cumulative frequency of the class before the median class, - \( f = 20 \) is the frequency of the median class, - \( h = 10 \) is the class width. Substitute these values into the median formula: \[ \text{Median} = 20 + \left( \frac{27.5 - 13}{20} \right) \times 10 = 20 + \left( \frac{14.5}{20} \right) \times 10 = 20 + 7.25 = 27.25. \]
Conclusion: The median of the given frequency distribution is \( 27.25 \).