Introduction to Outliers

Outliers are unusual data points that differ significantly from the majority of the data. They can occur due to data entry errors, natural variation, or rare but important events. Outliers can have a substantial impact on statistical summaries and modeling.

For example, a single large outlier can inflate the mean or distort the scale of visualizations, leading to misleading conclusions.

Understanding and detecting outliers is a critical step in data preprocessing. Depending on the goal of your analysis, you might choose to keep, transform, or remove outliers altogether.

Visualizing Outliers with Density Plots

A density plot provides a smooth curve that shows the distribution of a variable. Peaks indicate where data is concentrated, while long tails or isolated bumps might hint at outliers or skewness.

ggplot(df, aes(x = placement_exam_marks)) +
  geom_density(fill = "lightgreen", alpha = 0.7) +
  labs(title = "Density Plot Of Placement Exam Marks",
       x = "Placement",
       y = "Density") +
  theme_minimal()

Measuring Skewness

Skewness measures the degree of symmetry or asymmetry in a distribution. This helps detect whether a variable has outliers on one side of the distribution.

skewness(df$placement_exam_marks)

Interpretation of Skewness

• Skewness ≈ 0: approximately symmetric distribution;
• Skewness > 0: right-skewed distribution;
• Skewness < 0: left-skewed distribution;
• Skewness > 1: heavily right-skewed distribution;
• Skewness < -1: heavily left-skewed distribution.