For the data X: 5, 4, 3, 2, 1 and F: 1, 1, 2, 4, 5, what is the distribution shape?

• A. Symmetrical
• B. Positively skewed
• C. Negatively skewed
• D. Normal

Answer: (B)

Skewness describes where a distribution’s bulk sits and where its tail extends. In this set, most observations cluster at the low end (the value 1 occurs five times, then 2 occurs four times, 3 occurs twice, and only one observation each at 4 and 5). That puts the mass on the left side and creates a tail that stretches toward higher values on the right. The mean is pulled slightly above the median by that rightward tail (mean about 2.15, median 2), which is a hallmark of a positive (right) skew. It isn’t symmetric or normal because the data aren’t balanced around a central point—the left side dominates and the right tail is longer. So the distribution is positively skewed.