What characterizes a skewed distribution?

What characterizes a skewed distribution?

• A. The mean, median, and mode are equal
• B. Data is symmetrically distributed around the mean
• C. One tail is longer or fatter than the other
• D. The distribution forms a flat line

Answer: (C)

A skewed distribution is characterized by one tail being longer or fatter than the other. This imbalance in the tails indicates that the data is not symmetrically distributed around a central value. In a skewed distribution, the direction of the skew typically shows where the majority of the data points cluster. For example, if the distribution is skewed to the right (positively skewed), it has a longer tail on the right side, while the bulk of the data is on the left. Conversely, a left skew (negatively skewed) has a longer tail on the left side. This tail asymmetry impacts the relationship between the mean, median, and mode, often resulting in the mean being pulled in the direction of the skew. Understanding this characteristic helps in correctly interpreting the shape and behavior of the data set.

A skewed distribution is characterized by one tail being longer or fatter than the other. This imbalance in the tails indicates that the data is not symmetrically distributed around a central value. In a skewed distribution, the direction of the skew typically shows where the majority of the data points cluster. For example, if the distribution is skewed to the right (positively skewed), it has a longer tail on the right side, while the bulk of the data is on the left. Conversely, a left skew (negatively skewed) has a longer tail on the left side. This tail asymmetry impacts the relationship between the mean, median, and mode, often resulting in the mean being pulled in the direction of the skew. Understanding this characteristic helps in correctly interpreting the shape and behavior of the data set.