Boxplot analysis is a method of visually summarizing a dataset for understanding the spread, symmetry, and outliers of data at a glance. It can be used to analyze left-skewed and right skewed.
1. Key Terms to Know
- Interquartile Range (IQR): This is the “box” itself IQR = Q3 – Q1 it represents the middle 50% of your data.
- Outliers: Data points that fall far outside the expected range. In most software, an outlier is any point more than 1.5 X IQR away from the edges of the box. These are usually plotted as individual dots or asterisks.
- Whiskers: The lines extending from the box to the Minimum and Maximum. The most common method for determining whiskers is the Tukey Boxplot method, which uses the 1.5 X IQR.
| Component | What it Represents |
|---|---|
| Lower Whisker (Lower Fence) | Q1 – (1.5 X IQR) |
| First Quartile (Q1) | The 25th percentile; 25% of the data falls below this point. |
| Median (Q2) | The middle value; 50% of the data falls above and 50% below. |
| Third Quartile (Q3) | The 75th percentile; 75% of the data falls below this point. |
| Upper whisker (uppwer fence) | Q3 + (1.5 X IQR) |
2. How to Interpret the Analysis
When looking at a boxplot, you are performing a “visual audit” of your data’s behavior:
2.1 Analyzing Skewness
- Left-Skewed: The lower (left) whisker is longer, and the median is closer to the right of the box.
- Symmetrical: The whiskers are roughly the same length, and the median is in the center of the box.
- Right-Skewed: The upper (right) whisker is longer, and the median is closer to the left of the box.
2.2 Analyzing Variability
- Narrow Box: Indicates the data is very consistent and tightly grouped around the median.
- Wide Box: Indicates high variability; the data points are spread out across a large range.
Further Reading
You can refer to another tutorial on the difference between left-skewed and right-skewed.