Answer: Skewness measures the tendency of a larger amount of values moving in a given direction or with respect to the mean while the kurtosis measures how frequently a large observation of either sign are realized

**Correct Answer: A** **Explanation:** Skewness and kurtosis are both measures of the shape of a probability distribution: 1. **Skewness** measures the asymmetry of the distribution around its mean. It indicates whether the distribution is symmetric (skewness = 0) or has a longer tail on one side: - Positive skewness: Right-skewed distribution with a longer tail on the right - Negative skewness: Left-skewed distribution with a longer tail on the left - Skewness measures the tendency of values to cluster more on one side of the mean 2. **Kurtosis** measures the "tailedness" or peakedness of the distribution relative to a normal distribution: - High kurtosis: Distribution has heavy tails and a sharp peak (leptokurtic) - Low kurtosis: Distribution has light tails and a flat peak (platykurtic) - Kurtosis measures how frequently extreme observations (large deviations from the mean) occur **Why other options are incorrect:** - **Option B**: Incorrect because skewness can take any real value (positive, negative, or zero), not just between 0 and 1. Kurtosis is typically compared to 3 (for a normal distribution), but can also take various values. - **Option C**: Incorrect because skewness can be positive, negative, or zero, not always positive relative to kurtosis. - **Option D**: Incorrect because option A correctly describes the difference between skewness and kurtosis. **Key Distinction:** Skewness measures asymmetry (direction of tail), while kurtosis measures tail heaviness (frequency of extreme observations).

Author: Nikitesh Somanthe