To find the medians for the height and weight distributions, follow these steps:
### Step-by-step Solution
1. Collect the Data
- Heights (in centimeters): [tex]\(178, 163, 174, 186, 154, 167, 167, 181, 159, 165, 177, 191, 158\)[/tex]
- Weights (in pounds): [tex]\(157, 163, 190, 187, 183, 173, 184, 189, 193, 192, 177, 173, 168\)[/tex]
2. Sort the Data
- Heights: Sorted order: [tex]\(154, 158, 159, 163, 165, 167, 167, 174, 177, 178, 181, 186, 191\)[/tex]
- Weights: Sorted order: [tex]\(157, 163, 168, 173, 173, 177, 183, 184, 187, 189, 190, 192, 193\)[/tex]
3. Find the Median
- For an odd number of data points, the median is the middle value. In this case, both height and weight data have 13 points, which is odd.
- Median height: The 7th value in the sorted heights list is [tex]\(167\)[/tex].
- Median weight: The 7th value in the sorted weights list is [tex]\(183\)[/tex].
So, the correct medians for the height and weight distributions are:
- Median height: [tex]\(167\)[/tex]
- Median weight: [tex]\(183\)[/tex]
Therefore, the correct answer is:
C. [tex]\(167, 183\)[/tex]