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

Statistical Shorts

Age 11 to 16
Challenge Level Yellow star
Secondary curriculum
  • Problem
  • Getting Started
  • Student Solutions
  • Teachers' Resources

Statistical Shorts printable sheet
 

Below are some statistical statements. Can you decide whether each is always, sometimes, or never true?

If they are sometimes true, give examples or conditions under which they are true and under which they are false. 

If they are always true or never true, give convincing reasons why that is the case.

Be sure to be clear about your statistical assumptions in each case.

  1. It is just as likely to rain tomorrow as it is to rain the day after tomorrow.
  2. In a school, there will be two people who share a birthday.
  3. In a school, it will be someone's birthday every day.
  4. A randomly selected person from London will live to a greater age than a randomly selected person from Calcutta.
  5. If everyone in the class rolled two dice until someone threw a double six, there would be one winner.
  6. If I roll a die 100 times, I will get about the same number of 1s as 6s.
  7. If I flip a fair coin 20 times, I will get 10 heads.
  8. The mean, median and mode of a set of numbers can't all be the same.
  9. The mean cannot be less than both the median and the mode.
  10. Half of the students taking a test score less than the average mark.
  11. Nobody scores higher than the average mark in a test.
  12. In a game where you can only score an even number of points (0, 2, 10 or 50), the average score over a series of games must be an even number.

Could you adapt any of the statements that are sometimes true to make them always or never true?

 

This resource is part of the collection Statistics - Maths of Real Life

You may also like

Bat Wings

Two students collected some data on the wingspan of bats, but each lost a measurement. Can you find the missing information?

Mediant Madness

Kyle and his teacher disagree about his test score - who is right?

Kate's Date

When Kate ate a giant date, the average weight of the dates decreased. What was the weight of the date that Kate ate?

  • 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