Survey Analysis

Combinatorics · Axiom Academy

How market researchers use inclusion-exclusion to analyze overlapping customer preferences You're a data analyst at a streaming service company. Your team just surveyed 500 customers about their current subscriptions. The results show: Your manager asks: "How many unique customers subscribe to at least one of these services?" Your first thought might be to add them up: 285 + 240 + 195 = 720 customers. But wait... you only surveyed 500 people! The issue is that many customers subscribe to multiple services . When we add the totals, we're counting the same people multiple times! The overlapping regions represent customers with multiple subscriptions To find the real answer, we need more detailed data about the overlaps. The survey also collected: Here's the full breakdown from your survey: Before we calculate, think about this: If someone subscribes to all three services, how many times are they counted when we add up the two-service overlaps? The Inclusion-Exclusion Principle This is where the inclusion-exclusion principle comes in. It's a formula that corrects for overcounting when sets overlap: Where A = Netflix, B = Spotify, C = YouTube Premium Let's break down what this formula does: Result: Out of 500 surveyed customers, 445 subscribe to at least one service , and 55 subscribe to none of these three. Adjust the overlap values below and see how the total changes using inclusion-exclusion: The inclusion-exclusion principle appears everywhere in data analysis:

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