The following is the distribution of ages (in years) of children in a group:

What is the median age (in years) of children ?

Correct option is C

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$$\textbf{Given :} \\\ \, \\\text{Ages } = 3, 4, 6, 7, 8, 10 \\\ \, \\\text{Frequencies } = 9, 6, 4, 3, 5, 11 \\\ \, \\\textbf{Formula Used :} \\\ \, \\\text{Median} =\frac{\left(\frac{N}{2}\right)^{\text{th}} + \left(\frac{N}{2}+1\right)^{\text{th}}}{2} \\\ \, \\\textbf{Solution :} \\\ \, \\\text{Cumulative frequencies:} \\\ \, \\3 \rightarrow 9 \\\ \, \\4 \rightarrow 15 \\\ \, \\6 \rightarrow 19 \\\ \, \\7 \rightarrow 22 \\\ \, \\8 \rightarrow 27 \\\ \, \\10 \rightarrow 38 \\\ \, \\N = 38 \\\ \, \\\frac{N}{2} = 19,\ \frac{N}{2}+1 = 20 \\\ \, \\19^{\text{th}} \text{ observation} = 6 \\\ \, \\20^{\text{th}} \text{ observation} = 7 \\\ \, \\\text{Median} = \frac{6 + 7}{2} = 6.5 \\\ \, \\\textbf{Final Answer :} \\\ \, \\6.5$$​​