---
title: "Skewed data and skewness"
subject: "Data Mining"
chapter: 2
key: "semester_7/data_mining:skewed-data"
source: https://www.bctengineer.com/q/semester_7/data_mining/skewed-data
site: BCT Engineering
---

# Skewed data and skewness

Data Mining · Chapter 2: Data Pre-processing

- Asked in: year not given
- Video: [Statistics-Left Skewed And Right Skewed Distribution And Relation With Mean, Median And Mode](https://www.youtube.com/watch?v=0djtjjy12fI) — Krish Naik
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/data_mining/skewed-data
- Whole chapter: https://www.bctengineer.com/md/semester_7/data_mining/chapter-2

## Question

What do you mean by skewed data? Describe positive and negative skewness. Why are real-life data skewed?

## Short answer

Skewed data has an asymmetric distribution. Positive skew has a long right tail (mode < median < mean); negative skew has a long left tail (mean < median < mode). Real-life data are skewed due to natural lower limits, extreme values, and multiplicative processes.

## Answer

**Skewed data** is data whose distribution is not symmetric about its mean: one tail of the distribution is longer than the other. The **skewness** measures this asymmetry (0 for a symmetric distribution such as the normal one).

#### Positive (right) skew
- The tail is longer on the right; a few very large values pull the mean up.
- Relation: **mode < median < mean**.
- *Examples*: income, house prices, number of website visits per user.

#### Negative (left) skew
- The tail is longer on the left; a few very small values pull the mean down.
- Relation: **mean < median < mode**.
- *Examples*: marks in an easy exam (most students score high), age at death in developed countries.

```text
 Positive skew          Symmetric          Negative skew
 |\                       /\                       /|
 | \___                  /  \                  ___/ |
 |     \____ tail      _/    \_          tail ____/  |
   mode<median<mean    mean=median=mode   mean<median<mode
```

#### Why real-life data are skewed
- Natural lower limit with no upper limit (income, price, time cannot be below zero but can be very large).
- A few extreme cases (rich people, big transactions, viral pages) exist beside many ordinary ones: "rich get richer" and power-law effects.
- Natural growth processes are multiplicative.
- Ceiling or floor effects in tests, and outliers or errors.

Skewed data affect the mean and many algorithms; they are often handled by log or square-root transformation, and by using median instead of mean.

## Check yourself

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

1. What is skewed data?
   A. Data with zero variance
   B. Distribution not symmetric about its mean, with one longer tail
   C. Data with missing values
   D. A normal distribution
   Answer: B. Skewness measures asymmetry; it is 0 for a symmetric distribution. (Key point: Skewed definition)

2. For positive (right) skew, which relation holds?
   A. mean < median < mode
   B. mean = median = mode
   C. mode < median < mean
   D. median < mode < mean
   Answer: C. A long right tail pulls the mean above the median. (Key point: Positive skew relation)

3. Which is a negatively skewed example?
   A. Income
   B. House prices
   C. Website visits per user
   D. Marks in an easy exam where most students score high
   Answer: D. Negative skew has a longer left tail; mean < median < mode. (Key point: Negative skew example)

4. Why is income data typically right-skewed?
   A. Natural lower limit of zero with no upper limit, and a few extreme high values
   B. Incomes are chosen symmetrically
   C. Mean is always below the median
   D. Measurement always adds a negative error
   Answer: A. Lower bound plus a few large cases create a right tail. (Key point: Why skewed)

## Related in Data Mining

- [Data warehouse schemas](https://www.bctengineer.com/question.md?key=semester_7%2Fdata_mining%3Adw-schema-types) — Data Mining, chapter 1
- [Define data warehousing and creation process](https://www.bctengineer.com/question.md?key=semester_7%2Fdata_mining%3Adw-creation-process) — Data Mining, chapter 1
- [Dimension of data; curse of dimensionality](https://www.bctengineer.com/question.md?key=semester_7%2Fdata_mining%3Adimension-curse) — Data Mining, chapter 2
- [Data sampling methods](https://www.bctengineer.com/question.md?key=semester_7%2Fdata_mining%3Adata-sampling) — Data Mining, chapter 2
- [Confusion matrix and performance measures](https://www.bctengineer.com/question.md?key=semester_7%2Fdata_mining%3Aconfusion-matrix-measures) — Data Mining, chapter 3
- [Measures from confusion matrix (152, 130)](https://www.bctengineer.com/question.md?key=semester_7%2Fdata_mining%3Aconfusion-matrix-152-130) — Data Mining, chapter 3

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