Here is a fair six-sided die. If we roll it 60 times, roughly how many sixes would you expect to see? And a bigger question: will you get exactly that number, every single time?

Theory says a six comes up 1 time in 6, so we predict 10 sixes in 60 rolls. A single roll is unpredictable, theory only tells us the pattern across many rolls, never the result of one throw. Hold that prediction ready. In the next step we roll live and watch the count settle.

Today we run the die live and record what happens. We'll roll in batches and watch the histogram build. First 20 rolls. Then on to 40. Then on to 60. Each time, we compare the tally of sixes against our predicted one-in-six. We say aloud whether the experimental fraction is getting closer to a sixth or still bouncing around.

Today's review puzzle has five clues — cracking one unlocks the next. Each clue uses a different skill from this whole data and chance module. Work each clue in order; write every answer clearly before you move on.

• Clue 1: A pie chart shows the favourite sport of 60 pupils. The GAA slice is exactly one quarter of the pie. How many pupils chose GAA?
• Clue 2: Five match scores are 6, 10, 8, 4 and 12. Find the mean score.
• Clue 3: On a fair six-sided die, place the chance of rolling an even number on the probability scale (as a decimal).
• Clue 4: A tally of 40 die rolls shows 10 sixes. Write the experimental probability of a six as a percentage.
• Clue 5: Build the mystery number like this — take half of clue 2's answer (clue 3 tells you that half), add clue 1, then add clue 4. What mystery number do you get?

One pupil records at the board while the class checks each answer before the next clue is revealed.