Chapter 24: Review

Resolve the chapter problem

Plan a survey across the whole school, using a sample that includes different year groups and travel methods. Ask a neutral question such as “How did you travel to school today?” Record answers in a frequency table. A bar chart compares the travel categories. If you repeat the survey monthly, a time-series line graph can show changes. State that a sample estimate may differ from the full population.

Compare your first prediction with a suitable survey result. The prediction was a starting idea, not a test score.

Mixed practice

For each item, choose the method and explain why it fits.

1. A club asks a random sample of 40 members; 10 cycle. Estimate the proportion of all 360 members who cycle. Method: sample proportion.
2. A tally records 12 red, 8 blue and 10 green counters. Choose a chart to compare category counts. Method: bar chart.
3. Find the mean and range of $4, 5, 5, 6, 10$. Method: summary measures.
4. Values 1, 2 and 4 have frequencies 3, 2 and 1. Find the mean. Method: weighted mean.
5. A temperature record is 12°C, 15°C, 13°C over three days. Describe its time pattern. Method: read consecutive changes on a line graph.
6. A bag contains 3 red and 5 blue counters. Find the probability of red. Method: favourable outcomes over total outcomes.
7. A rectangle has length 8 cm and width 3 cm. Find its area. Method: area of a rectangle.

Reflect

Which measure or chart can you now choose with a reason? Name one point you would check before trusting a sample or graph.