To determine the shape of the height and weight distributions, we need to analyze their skewness. Skewness measures the asymmetry of the probability distribution of a real-valued random variable about its mean. It helps us understand if the data is skewed to the left (negative skew) or to the right (positive skew).
### Understanding Skewness Values:
1. Positive Skew (Right Skew):
- When skewness is greater than 0.
- The right tail (larger values) is longer, and most values are concentrated on the left.
2. Negative Skew (Left Skew):
- When skewness is less than 0.
- The left tail (smaller values) is longer, and most values are concentrated on the right.
3. Symmetric Distribution:
- When skewness is approximately 0.
- The distribution is symmetric around the mean.
Given the skewness values:
- The skewness for the height distribution is approximately 0.256.
- The skewness for the weight distribution is approximately -0.510.
### Interpreting the Results:
- Height Distribution Skewness: 0.256
- This value is positive, indicating that the height distribution is positively skewed (right skew).
- Weight Distribution Skewness: -0.510
- This value is negative, indicating that the weight distribution is negatively skewed (left skew).
### Conclusion:
- The height distribution has a positive skew (right skew).
- The weight distribution has a negative skew (left skew).
Based on this analysis, the correct answer is:
E. The height and weight distribution exhibit a positive and a negative skew, respectively.
