Question

Consider the following sample of numbers: \[ 9, 18, 11, 14, 15, 17, 10, 69, 11, 13 \] The median of the sample is:

• A. \( 13.5 \)
• B. \( 14 \)
• C. \( 11 \)
• D. \( 18.7 \)

Hint:

To find the median:
1. Arrange the data in ascending order.
2. For an odd number of values, select the middle value.
3. For an even number of values, average the two middle values.
4. Always double-check the ordering for accuracy.

Answer 1

The Correct Option is A

Step 1: Arrange the numbers in ascending order. The given sample is: \[ 9, 18, 11, 14, 15, 17, 10, 69, 11, 13 \] Arranging in ascending order: \[ 9, 10, 11, 11, 13, 14, 15, 17, 18, 69 \] Step 2: Determine the median. The median is the middle value of the ordered data. For a dataset with \( n \) values: - If \( n \) is odd, the median is the \((n+1)/2\)-th value. - If \( n \) is even, the median is the average of the \( n/2 \)-th and \((n/2)+1\)-th values. Here, \( n = 10 \) (even). The \( n/2 \)-th value is the 5th value: \( 13 \). The \((n/2)+1\)-th value is the 6th value: \( 14 \). Thus, the median is: \[ \text{Median} = \frac{13 + 14}{2} = 13.5 \] Conclusion: The median of the sample is \( \mathbf{13.5} \), corresponding to option \( \mathbf{(A)} \).