Question:
Find the median of the following data.
Find the median of the following data.
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For a discrete frequency distribution, use cumulative frequencies to identify the middle observations.
Updated On: Jun 15, 2026
- 6
- 7
- 8
- 7.5
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The Correct Option is B
Solution and Explanation
Step 1: Find total frequency.
\[ N = 8 + 9 + 10 + 11 = 38 \] Since \(N\) is even, \[ \text{Median} = \frac{\text{19th observation} + \text{20th observation}}{2} \]
Step 2: Locate observations using cumulative frequencies.
\[ \begin{array}{c|c} \text{Value} & \text{Cumulative Frequency} \\ \hline 5 & 8 \\ 6 & 17 \\ 7 & 27 \\ 8 & 38 \end{array} \] Both the 19th and 20th observations lie in the value 7. Hence, \[ \text{Median} = \frac{7 + 7}{2} = 7 \] \[ \boxed{7} \]
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