Skew

As explained in Effective Data Analysis

Skewness is the degree and direction to which a distribution is asymmetric around its center.

Skewness measures the degree and direction of asymmetry in a distribution around its center. It adds information about shape that a mean or median alone can miss. section 4.1.1

Use skewness to interpret summary statistics responsibly:

• Compare the mean, median, and other summaries with the distribution’s shape rather than treating one number as sufficient. section 4.1.1
• Recognize that skewed data and outliers can substantially affect the mean, while the median is more robust. section 4.1.1
• Check skewness and related assumptions before applying inferential tests, especially tests that assume normally distributed data. section 4.1.1 section 4.4

Mean and median under skew

Two distributions can have similar medians while differing greatly in shape. In a skewed distribution, the mean and median noticeably diverge; replacing a high outlier with a typical value changes the mean but leaves the median unchanged. section 4.1.1

Figure 4.3 The shape of a distribution can vary widely, and different summary statistics will give you clues about those shapes.

Compare distribution shapes that share similar summary values to see why skewness belongs in data reporting. section 4.1.1

How Effective Data Analysis covers it

How deep it goes

Treats skewness as a normality measure and links it to summary-statistic interpretation, but does not develop its calculation.

Examples

Uses contrasting distribution figures and mean–median comparisons involving skewed data and an extreme value.

What it assumes

Assumes familiarity with mean, median, and basic summary statistics while treating distribution assumptions as practical evaluation criteria.

What you can do after

Evaluate distribution shape, interpret means and medians cautiously, and identify when normality assumptions require attention.

How it connects

Connects skewness with central tendency, variability, normality, symmetry, outliers, and parametric statistical tests.

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Also explained in

• 

  liveBookmanning.com
  Modern CSkew is a statistical measure of the asymmetry or lopsidedness of a distribution.
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  liveBookmanning.com
  Modern C, Third EditionSkew measures the asymmetry or lopsidedness of a distribution around its mean.
• 

  liveBookmanning.com
  Statistics Slam DunkSkewness is the asymmetry of a probability distribution around its center.
• 

  liveBookmanning.com
  Machine Learning for Tabular Data: XGBoost, Deep Learning, and AIA probability or empirical distribution that is asymmetric around its central tendency.

Compare how 5 books explain skew →

Related concepts

• symmetrymeasures · Symmetry is the preservation of relevant structure or properties under a specified transformation, such as reflection, exchange, or reversal.
• log transformationaddressed by · A log transformation maps numerical values through a logarithmic function, changing their scale and often compressing large values or converting multiplicative relationships to additive ones.
• Gini coefficientcontrasts with · A Gini coefficient is a summary measure of inequality derived from the area between a Lorenz curve and the line of perfect equality, typically ranging from zero for complete equality toward one for greater inequality.
• density plotmeasured by · A density plot is a visualization that estimates and displays the shape of a continuous variable’s probability distribution as a smooth curve.
• raw momentproduced by · A raw moment is a statistical quantity formed from a specified power of observations measured relative to zero, typically by summing or averaging those powers.
• right-skewed distributionmeasures · A right-skewed distribution has most probability mass or observations at lower values and a comparatively long tail toward higher values.

This explainer was generated by Manning's knowledge graph from the text of Effective Data Analysis. The section links point to the parts of the book it draws on.