To find the value of \(20M\), where \(M\) is the median of the given frequency distribution, follow these steps:
Identify the total number of observations \(N\), which is the sum of all frequencies: \(N=2+4+7+8+6=27\).
Find the median class. The median position is \(\left(\frac{N}{2}\right)^{\text{th}}\) value, i.e., the \(13.5^{\text{th}}\) value. Cumulative frequencies: \(2, 6, 13, 21, 27\). Hence, the median class is \(12-16\) because \(13.5\) falls in this class.
Apply the median formula: \(M=L+\left(\frac{\frac{N}{2}-F}{f_m}\right) \cdot h\), where \(L\) is the lower boundary of the median class (\(12\)), \(F\) is cumulative frequency before the median class (\(13\)), \(f_m\) is the frequency of the median class (\(8\)), and \(h\) is the class width (\(4\)).
