Explanation

You should begin by considering the nature of your data—whether the variables are numeric, categorical, or mixed, and whether the dataset is low‑dimensional or high‑dimensional. For univariate numeric features, classic statistical rules such as the Z‑score (flagging |Z| > 3) or the interquartile range (IQR) method (points outside Q1 − 1.5·IQR or Q3 + 1.5·IQR) work well, especially when the data are roughly symmetric. If the distribution is skewed or heavy‑tailed, a robust measure like the median absolute deviation (MAD) provides a more reliable cutoff. Visual tools—box plots, histograms, scatter plots—help you spot obvious anomalies and communicate findings to stakeholders.

When the data have many dimensions, simple univariate rules miss multivariate outliers that only appear abnormal in combination. In such cases you can use algorithmic detectors: Isolation Forest builds random trees that isolate points quickly, assigning higher anomaly scores to points that require fewer splits; Local Outlier Factor (LOF) compares local densities; One‑Class SVM learns a boundary around the bulk of the data. For time‑series, you might decompose the series (e.g., STL) and flag large residuals, or use rolling Z‑scores. After flagging, always validate with domain knowledge, decide whether to remove, transform, or cap the outliers, and document the impact on downstream analysis.

Naive Response

I would just glance at the data, maybe draw a box plot, and delete any points that look far away. I might also use a Z‑score threshold of 2 and call those outliers. That's all I need.

Good Response

I would start by examining the distribution of each variable. For univariate numeric data, I would compute Z‑scores and flag observations with absolute Z > 3, or use the interquartile range (IQR) method, flagging points below Q1 − 1.5·IQR or above Q3 + 1.5·IQR. For skewed data, I would use the median absolute deviation (MAD) because it is robust to non‑normality. I would also generate visualizations—box plots, histograms, scatter plots—to spot obvious anomalies.

If the dataset is multivariate or high‑dimensional, I would apply algorithmic detectors such as Isolation Forest, Local Outlier Factor, or One‑Class SVM, which consider the joint distribution of features. For time‑series data, I would look at rolling statistics and use methods like STL decomposition to isolate outliers in the residual component. After flagging candidates, I would cross‑check with domain knowledge, assess the impact of removing or capping them, and document the rationale.

Why the Good Response is Better

It covers both univariate and multivariate techniques, matching the data’s dimensionality.
It explains why robust statistics (MAD) are preferred for skewed data, adding nuance missing in the naive answer.
It mentions validation with domain expertise and the decision process for handling outliers, not just detection.
The response is structured, uses concrete thresholds, and connects methods to practical steps.

283. Outlier Detection Methods

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