IGCSE Math RevisionBig tournament statistics for IGCSE and GCSE
A ready-to-teach statistics lesson for the summer term, built on a made-up tournament: a 5-minute starter, a 35-minute main activity on goals per match, shots and goals and probability, an extension and full worked answers. All the data are made up for this lesson.
- Level
- IGCSE and GCSE (Higher and Extended)
- Time
- 40 minutes, plus a 10-minute extension
- Topics
- Averages from a frequency table; Scatter graphs and lines of best fit; Relative frequency and expected outcomes; Combined means
- Equipment
- The starter is non-calculator. A calculator is allowed in the main activity.
Suggested timings
| Part | Time | What |
|---|---|---|
| Starter | 5 min | Quick questions on the board |
| Main: task A | 12 min | Goals per match |
| Main: task B | 12 min | Shots and goals |
| Main: task C | 11 min | Chance |
| Extension | 10 min | Fast finishers or homework |
Starter (5 minutes)
No calculator.
- Find the mean of 2, 4, 4, 5, 10.
- Find the median of 3, 8, 1, 9, 4, 7.
- Find the range of 12, 15, 9, 20, 17, 11, 14, 22, 8, 18.
- Find the mode of 2, 3, 3, 5, 7, 3.
Main activity (35 minutes)
Task A: Goals per match (12 min)
Made-up goals in 40 matches: 0 goals in 4 matches, 1 in 9, 2 in 11, 3 in 8, 4 in 5, 5 in 2 and 6 in 1.
- Check that there are 40 matches, and find the total number of goals.
- Find the mean number of goals per match.
- Find the median and the mode.
Task B: Shots and goals (12 min)
Made-up data for ten teams. Shots on target: 12, 15, 9, 20, 17, 11, 14, 22, 8, 18. Goals: 4, 5, 2, 8, 6, 3, 5, 9, 2, 6 (in the same order).
- Plot a scatter graph. Find the mean number of shots and the mean number of goals.
- A line of best fit passes through the mean point (14.6, 5) and the point (8, 2). Find its gradient, to 3 significant figures.
- Use the line to estimate the goals for a team with 16 shots on target, to 1 decimal place.
Task C: Chance (11 min)
Use the goals table from task A.
- Find the relative frequency of a match with 3 or more goals.
- The next stage has 64 matches. How many would you expect to have 3 or more goals?
- Using relative frequency, estimate the probability that two matches, independently, both have no goals.
Extension (10 minutes)
For fast finishers, or as homework.
- After 8 more matches, the mean number of goals over all 48 matches is 2.5. How many goals were scored in the 8 new matches?
- Find the mean number of goals in those 8 new matches, as a decimal.
For teachers
Teacher notes and full worked answers
- Every number in this pack is made up for the lesson; say so when you show it.
- In task B, ask why a line of best fit through the mean point is a good choice.
- Task C (b): the expected number need not be a whole number.
Starter
- 5
- 25 ÷ 5 = 5
- 5.5
- 1, 3, 4, 7, 8, 9: (4 + 7) ÷ 2 = 5.5
- 14
- 22 − 8 = 14
- 3
- 3 appears most often.
Task A: Goals per match
- 40 matches; 91 goals
- 4 + 9 + 11 + 8 + 5 + 2 + 1 = 40
- 0 × 4 + 1 × 9 + 2 × 11 + 3 × 8 + 4 × 5 + 5 × 2 + 6 × 1 = 91
- 2.275
- 91 ÷ 40 = 2.275
- Median 2; mode 2
- The median is halfway between the 20th and 21st values. The running totals are 4, 13, 24, …, so both are 2.
- The most common number of goals is 2 (11 matches).
Task B: Shots and goals
- 14.6 and 5
- 146 ÷ 10 = 14.6 and 50 ÷ 10 = 5
- 0.455
- (5 − 2) ÷ (14.6 − 8) = 3 ÷ 6.6 = 0.4545…
- 5.6 goals
- 5 + 0.4545… × (16 − 14.6) = 5.636…
Task C: Chance
- 2/5
- 8 + 5 + 2 + 1 = 16 matches; 16/40 = 2/5
- 25.6, so about 26
- 64 × 2/5 = 25.6
- 1/100
- P(0 goals) = 4/40 = 1/10, so (1/10)2 = 1/100.
Extension
- 29
- 48 × 2.5 = 120 goals in all.
- 120 − 91 = 29
- 3.625
- 29 ÷ 8 = 3.625
The same answers are in the answers PDF. Every answer was recomputed by computer before publishing.
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