How Quantities Combine: Understanding Data
Class 9 · Mathematics
3 ideas in Class 9 Mathematics, explained in plain words, with games and quizzes to practise.
Weighted Averages
Part of: Weighted Averages
A weighted average gives more influence to groups containing more values. Multiply each group average by its size, add those totals and divide by the total size.
Why it matters. Treating small and large groups equally can distort the overall result.
Try it in two minutes
- Make two groups of counters with different sizes.
- Give each group a different average value.
- Combine totals before finding the new average.
Try at home. Ask whether two reported averages represent groups of equal size.
Mixtures and Custom Weights
Part of: Mixtures and Custom Weights
A mixture’s final concentration depends on how much of each mixture is used. A rating score can be combined similarly by giving each feature a chosen weight.
Why it matters. Weighted averages are useful for mixtures, marks and rating systems where parts contribute in different amounts.
Try it in two minutes
- Mix two coloured water samples in different quantities.
- Notice which sample contributes more to the final colour.
- Give more important rating features larger weights.
Try at home. Try a weighted score with two criteria, such as comfort and travel time.
Stacked Charts and Proportions
Part of: Stacked Charts and Proportions
A stacked chart shows both parts and total amounts. A 100% stacked chart makes each bar the same full length, so it compares proportions rather than absolute totals.
Why it matters. Choosing the right chart prevents a misleading comparison between large totals and large shares.
Try it in two minutes
- Draw two bars with different totals and divide each into parts.
- Make a second version with equal full lengths.
- Ask which version shows totals and which shows shares.
Try at home. When you see a chart, ask whether it compares counts or percentages.
What your child will practise
- Mixtures and Custom Weights: Desert Quick Fire (Quick Fire)
- Mixtures and Custom Weights: Jungle Puzzle (Clue Puzzle)
- Stacked Charts and Proportions: Mission Control Sort (Sort It Out)
- Stacked Charts and Proportions: Space Quick Fire (Quick Fire)
- Weighted Averages: Number Quest (Collect the Answer)
- Quiz: Mixtures and Custom Weights (8 questions)
- Quiz: Stacked Charts and Proportions (8 questions)
- Quiz: Weighted Averages (8 questions)