Skip over navigation
Cambridge University Faculty of Mathematics NRich logo
menu search
  • Teachers expand_more
    • Early years
    • Primary
    • Secondary
    • Post-16
    • Events
    • Professional development
  • Students expand_more
    • Primary
    • Secondary
    • Post-16
  • Parents expand_more
    • Early Years
    • Primary
    • Secondary
    • Post-16
  • Problem-Solving Schools
  • About NRICH expand_more
    • About us
    • Impact stories
    • Support us
    • Our funders
    • Contact us
  • search

Or search by topic

Number and algebra

  • The Number System and Place Value
  • Calculations and Numerical Methods
  • Fractions, Decimals, Percentages, Ratio and Proportion
  • Properties of Numbers
  • Patterns, Sequences and Structure
  • Algebraic expressions, equations and formulae
  • Coordinates, Functions and Graphs

Geometry and measure

  • Angles, Polygons, and Geometrical Proof
  • 3D Geometry, Shape and Space
  • Measuring and calculating with units
  • Transformations and constructions
  • Pythagoras and Trigonometry
  • Vectors and Matrices

Probability and statistics

  • Handling, Processing and Representing Data
  • Probability

Working mathematically

  • Thinking mathematically
  • Developing positive attitudes
  • Cross-curricular contexts

Advanced mathematics

  • Decision Mathematics and Combinatorics
  • Advanced Probability and Statistics
  • Mechanics
  • Calculus

For younger learners

  • Early Years Foundation Stage

Friendship Paradox

Age 11 to 16
  • Project

This classroom activity is part of the Disease Dynamics collection




This activity shows that more than just disease dynamics can be gleaned from analysing network structures.

Although networks are vital for understanding disease transmission in a population, they can be used for several other uses beyond public health.  This can include sociology, psychology, criminology, political science, computer science etc.

This activity builds on work by sociologist Scott Feld (Feld S, (1991) Why Your Friends Have More Friends Than You Do, American Journal of Sociology, Vol 96, No 6. (May 1991) pp 1464-1477) to show that on average, your friends have more friends than you.


Resources: Slides (PowerPoint or PDF), Printable Friendship Graph (PowerPoint or PDF)

Curriculum Link

Maths:
  • Describe, interpret and compare observed distributions of a single variable through graphical representations, as well as mean, median, mode, range and outliers.


Aims


  • To establish that you can learn a variety of things from network analysis
  • To revisit averages


Activities (Small Groups)



Start with person 1 and count the number of friends they have.

Count how many friends each of their friends have, and calculate the average number of friends they have.

Complete with all of the people in the network; the chart can be printed out for students to fill in.




Questions for thought


Does this surprise you?

What else could you analyse on a network?
  • Tech help
  • Accessibility Statement
  • Sign up to our newsletter
  • Twitter X logo

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

University of Cambridge logo NRICH logo