Central Tendency & DispersionPYQ Dec 23Question 2961 of 473
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For a given data set: 5,10,3,6,4,8,9,3,15,2,9,4,19,11,4\displaystyle 5, 10, 3, 6, 4, 8, 9, 3, 15, 2, 9, 4, 19, 11, 4, what is the median?

Options

A8\displaystyle 8
B6\displaystyle 6
C4\displaystyle 4
D9\displaystyle 9
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Correct Answer

✅ Option b — 6\displaystyle 6

All Options:

  • A8\displaystyle 8
  • B6\displaystyle 6
  • C4\displaystyle 4
  • D9\displaystyle 9

Detailed Solution & Explanation

We are given the data set: 5,10,3,6,4,8,9,3,15,2,9,4,19,11,4\displaystyle 5, 10, 3, 6, 4, 8, 9, 3, 15, 2, 9, 4, 19, 11, 4. 1. Arrange the data in ascending order: 2,3,3,4,4,4,5,6,8,9,9,10,11,15,192, 3, 3, 4, 4, 4, 5, 6, 8, 9, 9, 10, 11, 15, 19 Here, the number of observations is n=15\displaystyle n = 15 (which is odd). 2. The median is the n+12th\displaystyle \frac{n+1}{2}^{\text{th}} observation: Position of Median=15+12=8th observation\text{Position of Median} = \frac{15 + 1}{2} = 8^{\text{th}} \text{ observation} 3. The 8th\displaystyle 8^{\text{th}} observation in the sorted list is 6\displaystyle 6. Therefore, the median of the dataset is 6\displaystyle 6. Hence, **Option B** is the correct answer.

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