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).