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Gabe is the human resources manager for the Advanced Scientific Research Lab. He has recorded the heights (in centimeters) and weights (in pounds) for each of the scientists in the lab.

| Height (cm) | 178 | 163 | 174 | 186 | 154 | 167 | 167 | 181 | 159 | 165 | 177 | 191 | 158 |
|-------------|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|
| Weight (lbs)| 157 | 163 | 190 | 187 | 183 | 173 | 184 | 189 | 193 | 192 | 177 | 173 | 168 |

What are the medians for the height and weight distribution, respectively?

A. 170, 179
B. 183, 167
C. 167, 183
D. 179, 170
E. 165, 175

Sagot :

GinnyAnswer
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]
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