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 \( N = 33 \). The median class corresponds to the cumulative frequency just greater than \( \frac{N}{2} = \frac{33}{2} = 16.5 \). The median class is the one with the cumulative frequency 19, which corresponds to the class interval \( 55-60 \). Now, we use the median formula: \[ \text{Median} = L + \left( \frac{\frac{N}{2} - F}{f} \right) \times h, \]
where:
- \( L = 55 \) is the lower limit of the median class, - \( F = 13 \) is the cumulative frequency of the class before the median class, - \( f = 6 \) is the frequency of the median class, - \( h = 5 \) is the class width. Substituting the values: \[ \text{Median} = 55 + \left( \frac{16.5 - 13}{6} \right) \times 5 = 55 + \left( \frac{3.5}{6} \right) \times 5 = 55 + 2.9167 \approx 57.92. \]
Conclusion: The median of the given frequency distribution is approximately \( 57.92 \).