---
title: "Graphical drawbacks; statistical approaches"
subject: "Data Mining"
chapter: 6
key: "semester_7/data_mining:anomaly-graphical-statistical"
source: https://www.bctengineer.com/q/semester_7/data_mining/anomaly-graphical-statistical
site: BCT Engineering
---

# Graphical drawbacks; statistical approaches

Data Mining · Chapter 6: Anomaly / Fraud Detection

- Asked in: year not given
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/data_mining/anomaly-graphical-statistical
- Whole chapter: https://www.bctengineer.com/md/semester_7/data_mining/chapter-6

## Question

List the drawbacks of graphical approach and describe statistical approaches for anomaly detection.

## Short answer

Graphical detection is subjective, not scalable, limited to low dimensions, and unsuited to real-time use. Statistical approaches assume a distribution for normal data and flag low-probability objects; parametric methods use z-score, Mahalanobis distance, mixtures, or Grubbs' test, while non-parametric methods use histograms or kernel density estimates.

## Answer

#### Graphical approach and its drawbacks
In the graphical approach, data are drawn as **box plots** (outliers beyond 1.5 × IQR), **scatter plots**, histograms or Q-Q plots, and a person visually identifies the points that lie apart from the rest.

**Drawbacks**
- **Subjective**: depends on the person's judgment; no clear formal definition of an outlier.
- **Not scalable**: impractical for large data sets, and not automatic.
- Limited to **low dimensions** (1-3 attributes), where we can plot.
- Not usable for **real-time/streaming** detection, and cannot give a numeric degree of outlierness.
- Different people may give different results.

#### Statistical approaches
These assume a **statistical model** (distribution) for the normal data. An object that has a **low probability** under the model, i.e. does not fit it, is an outlier.

1. **Parametric methods**
   - *Univariate normal distribution*: compute mean μ and standard deviation σ; objects with |x − μ|/σ > 3 (z-score) lie outside μ ± 3σ and are outliers (about 0.3% of normal data).
   - *Multivariate*: use the Mahalanobis distance or χ² statistic to the mean; large distance means an outlier.
   - *Mixture of distributions*: normal data is from distribution F_N, anomalies from a different distribution F_A; the object is assigned to the more probable one (likelihood approach).
   - *Grubbs' test* for one outlier at a time.
2. **Non-parametric methods**: no assumed distribution; the model is learnt from the data, e.g. a **histogram** or kernel density estimate. An object falling in a bin with a very low frequency is an outlier.

**Strengths**: well founded in theory, give a confidence level; efficient when the distribution is known. **Weaknesses**: most tests are for a single attribute; the data distribution is often not known; poor for high dimensions.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Which is a drawback of the graphical approach?
   A. It is objective and automatic
   B. It is subjective and limited to low dimensions
   C. It works well on streaming data
   D. It gives numeric outlier degrees
   Answer: B. It depends on human judgment, does not scale and works only for 1-3 attributes. (Key point: Graphical drawbacks)

2. What is the core idea of statistical approaches?
   A. Objects far from neighbours are outliers
   B. Objects with low probability under a model of normal data are outliers
   C. Objects in small grid cells are outliers
   D. Objects in clusters are outliers
   Answer: B. They assume a distribution for normal data; poor fit means outlier. (Key point: Statistical idea)

3. In the univariate normal case, which objects are outliers?
   A. |x - mu|/sigma > 3
   B. |x - mu|/sigma < 1
   C. x < 0
   D. x equal to mu
   Answer: A. Points outside mu +/- 3 sigma are outliers. (Key point: Univariate rule)

4. How do non-parametric methods detect outliers?
   A. Assume a normal distribution
   B. Learn a model such as a histogram from data; objects in very low-frequency bins are outliers
   C. Use the Mahalanobis distance only
   D. Use class labels
   Answer: B. No distribution is assumed; e.g. histogram bins with very low frequency flag outliers. (Key point: Non-parametric)

## Related in Data Mining

- [Short note: Distance-based anomaly detection](https://www.bctengineer.com/question.md?key=semester_7%2Fdata_mining%3Adistance-based-anomaly-note) — Data Mining, chapter 6
- [Anomaly detection and importance](https://www.bctengineer.com/question.md?key=semester_7%2Fdata_mining%3Aanomaly-detection-intro) — Data Mining, chapter 6
- [Anomaly detection challenges and schemes](https://www.bctengineer.com/question.md?key=semester_7%2Fdata_mining%3Aanomaly-challenges-schemes) — Data Mining, chapter 6
- [Short note: Likelihood approach to anomalies](https://www.bctengineer.com/question.md?key=semester_7%2Fdata_mining%3Alikelihood-anomaly-note) — Data Mining, chapter 6

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