In the study of statistics, understanding the shape and distribution of data is crucial. While measures of Central Tendency (Mean, Median, Mode) and Measures of Dispersion (Range, Standard Deviation, Coefficient of Variation) help us understand the average and variability of data, they do not always tell the full story. For a more complete analysis, we also need to understand the concept of Skewness.
What is Skewness?
Skewness refers to the degree of asymmetry or departure from symmetry in the distribution of data. In simpler terms, it tells us whether the data is tilted to the left, to the right, or is perfectly symmetrical.
a. Symmetrical Distribution
In a symmetrical distribution, the values of mean, median, and mode are all equal. The graph of such a distribution is bell-shaped and evenly balanced on both sides.
b. Skewed Distribution
- Positively Skewed: The tail on the right side is longer. Mean > Median > Mode.
- Negatively Skewed: The tail on the left side is longer. Mean < Median < Mode.
Why Study Skewness?
Understanding skewness helps in:
- Identifying the direction and degree of asymmetry in data.
- Improving decision-making based on data behavior.
- Providing insights that central tendency and dispersion measures may overlook.
- Choosing suitable statistical techniques (some require normal distribution).
Key Measures of Skewness
There are several ways to measure skewness. Each method provides a numerical value that helps us understand the nature and direction of skewness in a dataset. These measures are broadly classified into two categories:
- Absolute Measures of Skewness:
- Mean – Median
- Mean – Mode
- Relative Measures of Skewness (Coefficients):
Types of Skewness
| Type of Skewness | Shape | Mean, Median, Mode Relation |
|---|---|---|
| Symmetrical | Bell-shaped | Mean = Median = Mode |
| Positively Skewed | Tail on right | Mean > Median > Mode |
| Negatively Skewed | Tail on left | Mean < Median < Mode |
Skewness in Real Life
- Income Distribution: Often positively skewed a small number of people earn much more than the majority.
- Exam Scores: Negatively skewed if most students score high and only a few score low.
- Sales Data: Could be skewed based on product popularity.
Next Steps in Your Learning
This article provides the conceptual foundation for understanding skewness. From here, we will explore each method of measuring skewness in detail. Click the links below to continue:
- Karl Pearson’s Coefficient of Skewness
- Bowley’s Coefficient of Skewness
- Kelly’s Coefficient of Skewness
- Moment-Based Measures of Skewness
Conclusion
Measures of Skewness provide valuable insights into the nature of data distribution. Whether symmetrical or skewed, understanding the direction and degree of skewness is essential for accurate analysis. As you continue exploring, keep in mind the relevance of each method and its applicability to different datasets. Let this foundation guide your deeper study into statistical methods of skewness.