Question

The median of the data \(13,\ 9,\ 11,\ 7,\ 17,\ 15,\ 5\) is:

• A. \(5\)
• B. \(7\)
• C. \(11\)
• D. \(15\)

Hint:

Always arrange the observations in ascending order before finding the median. For odd number of observations: \[ \text{Median} = \left( \frac{N+1}{2} \right)^{\text{th}} \text{ term} \]

Answer 1

The Correct Option is C

Concept: The median is the middle value of a data set after arranging the observations in ascending or descending order. For:
• Odd number of observations: \[ \text{Median} = \left( \frac{N+1}{2} \right)^{\text{th}} \text{ observation} \]
• Even number of observations: \[ \text{Median} = \frac{ \left(\frac{N}{2}\right)^{\text{th}} + \left(\frac{N}{2}+1\right)^{\text{th}} }{2} \]

Step 1: Arranging the data in ascending order.
The given observations are: \[ 13,\ 9,\ 11,\ 7,\ 17,\ 15,\ 5 \] After arranging in ascending order: \[ 5,\ 7,\ 9,\ 11,\ 13,\ 15,\ 17 \]

Step 2: Finding the total number of observations.
Total number of observations: \[ N = 7 \] Since \(N\) is odd, the median will be the middle observation.

Step 3: Finding the position of the median.
Using: \[ \text{Position of Median} = \left( \frac{N+1}{2} \right)^{\text{th}} \] Substituting \(N=7\): \[ = \left( \frac{7+1}{2} \right)^{\text{th}} \] \[ = \left( \frac{8}{2} \right)^{\text{th}} \] \[ = 4^{\text{th}} \text{ observation} \]

Step 4: Identifying the median value.
The ordered observations are: \[ 5,\ 7,\ 9,\ 11,\ 13,\ 15,\ 17 \] The \(4^{\text{th}}\) observation is: \[ 11 \] Therefore: \[ \text{Median} = 11 \]

Step 5: Checking the options carefully.
Option (1): \[ 5 \] Incorrect. Option (2): \[ 7 \] Incorrect. Option (3): \[ 11 \] Correct. Option (4): \[ 15 \] Incorrect. Final Conclusion: The median of the given data is: \[ \boxed{11} \] Hence, the correct answer is option (3).