Question

What is the median age of the 7 cows whose ages are listed below?
11, 10, 13, 11, 12, 16, 14

• A. 10
• B. 11
• C. 16
• D. 12

Hint:

Always sort the data before identifying the middle element.
For an odd number of observations, the median is always an actual value from the dataset.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The median is the middle value of a dataset when the observations are arranged in ascending or descending order.
Detailed Explanation:
Let us find the median of the given dataset:
\[ \text{Dataset: } \{11, 10, 13, 11, 12, 16, 14\} \] First, sort the values in ascending order:
\[ \text{Sorted Dataset: } \{10, 11, 11, 12, 13, 14, 16\} \] The number of observations (\( n \)) is \( 7 \), which is an odd number.
The median is the value at position:
\[ \text{Median Position} = \frac{n + 1}{2} = \frac{7 + 1}{2} = 4\text{th position} \] Identifying the value at the 4th position in the sorted list:
- 1st: 10
- 2nd: 11
- 3rd: 11
- 4th: 12
- 5th: 13
- 6th: 14
- 7th: 16
The value at the 4th position is 12, which is the median of the dataset.

Step 2: Final Answer:
The median age of the cows is 12.