Will one phone brand take over? Brand loyalty as a Markov chain

AI HL Solid Also in: Statistics, Probability, Finance

Research question

Using survey data on which brand students switched from and to at their last phone upgrade, what long-term market shares does a Markov chain predict, and how sensitive are they to loyalty rates?

Adapt it: change the place, the data or the comparison until the question is yours.

Why it makes a good exploration

Markov chains model any system where people move between states. Surveying real switching behaviour gives you a transition matrix built from your own data.

The mathematics you'll need

Transition matrices from survey data
Matrix powers for future shares
Steady-state vectors and eigenvectors
Sensitivity analysis

Course labels show where a technique sits; using maths from outside your course is fine if you explain it clearly and say it is new to you.

Where the data comes from

Survey 60+ people (students and adults) about their previous and current phone brand.

Desmos graphing calculator — Free graphing and regression (y₁ ~ ax₁ + b) — fit models to your data and show residuals.

Cite every source in a footnote where you use it and in your bibliography. Check the licence of any dataset you download.

A possible outline

Design the survey and define states.
Build the transition matrix.
Predict shares after several upgrades.
Find the steady state.
Reflect on sampling, new brands and changing loyalty.

Pitfalls that cost marks

Too few people in some categories.
Assuming transition probabilities stay constant without comment.
Rows/columns not summing to 1.

Showing personal engagement

Include your own switching story.
Compare with published market shares.
Test how a price change (a change in loyalty) affects the steady state.

See Criterion C: personal engagement for what examiners look for.

Taking it further

Compare the survey of students with a survey of adults and discuss which chain is more stable.

Turn this idea into your IA

Plan this IAOpens the planner with this question, the maths and data sources filled in. Desmos workspacePlot your data, fit models and keep your graphs with your plan. AI feedback on a draftCriterion-by-criterion feedback with evidence from your own text. Coaching, not rewriting. Examiner reviewPete, a practising IA examiner, reads your draft and talks it through with you (€100).