Why Averages Are (Almost) Always Wrong: Jensen's Inequality and the Flaw of Averages

Today's video provides an overview of the 'flaw of averages'. The basic premise is that feeding average values into a model or function will typically not yield an average response.

We'll show why this is the case, prove why this happens via Jensen's inequality, and see the 'flaw of averages' in action via a realistic problem! The portion on Jensen's inequality is likely of interest to anyone interested in data science given that it underlies many important theorems (e.g., KL divergence)!

0:00 Overview of Flaw of Averages
0:42 Expected Value Definition
1:36 'Average In' vs. 'Average Out' - 2 Examples
4:02 Jensen's Inequality Proof
7:38 Summary of Non-Linearity and Jensen's Inequality
8:18 Will You Arrive in 1 Hour?

#probability #datascience #average #mathematics #education #jensensinequality

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September 27, 2024: As I've mentioned in the last couple of videos, we now have a RiskByNumbers blog (riskbynumbers.org and riskbynumbers.com)! I've finally started putting together some written explainer drafts, and I'll be posting them shortly. Feel free to provide comments or feedback around the type of content you'd like to learn more about by commenting on this video or reaching out to me directly.

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If this is your first video, welcome! I am a professor sharing educational resources around probability, statistics, optimization methods, algorithms, and programming to a broad audience.

Outside of YouTube, you can currently find me in Vancouver, Canada at the University of British Columbia.

Thank you, and I look forward to seeing you in future videos!

Email: [email protected].
LinkedIn:   / omar-swei