3.13
Types of Skewness
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Q1: What does it mean when a distribution is negatively skewed?
A negatively skewed distribution occurs when a graph extends to the left side, forming a longer tail on the left. In this case, the mean and median are positioned to the left of the mode. An example is student scores on an easy exam, where fewer students score lower scores, creating a left-leaning tail in the distribution.
Q2: How does positively skewed data differ from negatively skewed data?
Positively skewed data extends to the right with a longer right tail, while negatively skewed data extends to the left with a longer left tail. In positive skewness, the mean and median lie right of the mode. In negative skewness, they lie left of the mode. Annual income distribution typically shows positive skewness, with most people earning lower incomes.
Q3: Where do the mean and median sit in a positively skewed distribution?
In a positively skewed distribution, both the mean and median are positioned to the right side of the mode. This rightward shift occurs because the longer tail on the right pulls these central tendency measures away from the peak. The mode remains at the distribution's highest point regardless of skewness direction.
Q4: What is zero skewness in a data distribution?
Zero skewness occurs when a graph has a symmetric or normal distribution, where the left half is a mirror image of the right half. In this case, the mean, median, and mode are all equal and centered. The data shows no tendency to lean toward either extreme, indicating perfect balance.
Q5: How can you identify skewness by looking at a graph?
Skewness is identified by observing whether the left and right halves of a distribution graph are mirror images. If the graph extends left with a longer tail, it is negatively skewed. If it extends right with a longer tail, it is positively skewed. A symmetric graph with no tail extension indicates zero skewness.
Q6: What real-world example demonstrates positive skewness?
Annual income distribution among city residents demonstrates positive skewness. A large number of people earn lower incomes, creating a concentration on the left side of the distribution with a long tail extending right toward higher earners. This right-leaning pattern is characteristic of many economic datasets in real populations.
Q7: Why does the mode stay at the peak regardless of skewness type?
By definition, the mode peaks at the distribution's highest point, representing the most frequently occurring value. Unlike the mean and median, which shift toward the direction of the skew, the mode remains anchored at the frequency peak. This makes the mode a stable reference point for comparing skewed distributions.