Skewness and Kurtosis
Measures of asymmetry and tail heaviness.
Key idea
Measures of asymmetry and tail heaviness.
In depth
Skewness measures asymmetry: positive means a long right tail, negative a long left tail. Kurtosis measures tail heaviness compared to the normal distribution. In right-skewed data, mean > median.
Worked example
Income is right-skewed: a few very high earners pull the mean above the median.
Real-world uses
- Checking whether income data is lopsided before choosing a statistical test
Common mistake
Assuming mean = median in all data.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Skewness and Kurtosis?
Measures of asymmetry and tail heaviness. It is a topic at the expert level in Probability & Statistics.
Where is Skewness and Kurtosis used in real life?
Real-world examples: Checking whether income data is lopsided before choosing a statistical test.
What should I learn before Skewness and Kurtosis?
Make sure you are comfortable with Percentiles and Z-Scores, the previous topic in Probability & Statistics.
What is a common mistake with Skewness and Kurtosis?
Assuming mean = median in all data.
How can I practise Skewness and Kurtosis?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Skewness and Kurtosis?
Move on to Scatter Plots next.
Related expert topics in Probability & Statistics
- Residuals and R² – Error of a fit and proportion of variance explained.
- Simpson’s Paradox – A trend reverses when groups are combined.
- Law of Total Probability – Split an event over a partition.
- Bayes’ Theorem – Update beliefs with evidence.
- Medical Tests and Base Rates – Why positive results can still be probably false.
- Linearity of Expectation – Expectation of sums is sum of expectations.