To determine the medians for the given height and weight distributions, we must follow these steps:
1. List the Heights and Weights:
The heights (in centimeters) are:
[tex]\[
178, 163, 174, 186, 154, 167, 167, 181, 159, 165, 177, 191, 158
\][/tex]
The weights (in pounds) are:
[tex]\[
157, 163, 190, 187, 183, 173, 184, 189, 193, 192, 177, 173, 168
\][/tex]
2. Sort the Height Values in Ascending Order:
Sorted heights:
[tex]\[
154, 158, 159, 163, 165, 167, 167, 174, 177, 178, 181, 186, 191
\][/tex]
3. Sort the Weight Values in Ascending Order:
Sorted weights:
[tex]\[
157, 163, 168, 173, 173, 177, 183, 184, 187, 189, 190, 192, 193
\][/tex]
4. Find the Median of the Heights:
- Since the number of height entries is 13 (odd), the median is the middle number.
- The middle number is the 7th value in this case (since [tex]\((13+1)/2 = 7\)[/tex]).
Hence, the height median is:
[tex]\[
167
\][/tex]
5. Find the Median of the Weights:
- Similarly, the number of weight entries is 13 (odd), so the median is the middle number.
- The middle number is the 7th value in this case (since [tex]\((13+1)/2 = 7\)[/tex]).
Hence, the weight median is:
[tex]\[
183
\][/tex]
The medians for the height and weight distributions are 167 cm and 183 lbs, respectively.
Therefore, the correct answer is:
[tex]\[
\boxed{C \; 167, 183}
\][/tex]
