The median of the observations $ 4, 14, 11, 9, 7, 8, 9, 12, 4 $ and $ 6 $ is:

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Examoogle · Accepted Answer

The correct answer is Option C: 8.5. Arrange the data in ascending order and pick the middle two values; their average is the median since the number of observations is even.

Step-by-Step Solution & Concepts:
Shortcut Trick: Arrange the data in ascending order and pick the middle two values; their average is the median since the number of observations is even.

Formula Used: $$Median = \begin{cases} \left(\frac{n+1}{2}ight)^{th} 	ext{ observation} & 	ext{if } n 	ext{ is odd} \ \frac{\left(\frac{n}{2}ight)^{th} + \left(\frac{n}{2}+1ight)^{th}}{2} 	ext{ observation} & 	ext{if } n 	ext{ is even} \end{cases}$$

Given: The observations are: 4, 14, 11, 9, 7, 8, 9, 12, 4, 6

Steps: Sort the observations: First, we arrange the given list of numbers {4, 14, 11, 9, 7, 8, 9, 12, 4, 6} in ascending order.. Count the total observations: Count the total number of terms, denoted by $n$. Here, $n = 10$, which is an even number.. Apply the median formula: Since $n = 10$ is even, the median is the average of the 5th and 6th terms.. Calculate the final result: The 5th term is $8$ and the 6th term is $9$. Taking the average of these two values gives the median: $(8 + 9) / 2 = 8.5$.

Answer: C is correct because the median of the sorted data set is 8.5.

Exam Tip: This concept is essential for the Mean-Median-Mode relationship in statistics and data interpretation questions frequently appearing in competitive exams.

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