NCERT Ganita Manjari, Class 9, textbook pages 8–36 (Part II)

How to help your child with Class 9 Maths Chapter 10, How Quantities Combine: Understanding Data, at home

Weighted averages, percentages and data displays, explained for parents: a 30-minute study session, a quick challenge, a 5-day plan and the mistakes to watch for.

(8 × 165.5 + 3 × 149.3) ÷ 11≈ 161.1 cmnot (165.5 + 149.3) ÷ 2

NCERT Class 9 Maths Chapter 10 How Quantities Combine: Understanding Data: what it teaches

The average of two group averages is not the average of everyone unless the groups are the same size. Your teen learns weighted averages, combines ratios and percentages correctly, and reads and draws data displays such as pie charts.

Why it matters later. Weighted averages are used in statistics, exam grading, economics and science.

See it: this chapter in pictures

avg of averages: (165.5 + 149.3)/2= 157.4 ✗groups differ in size
Group sizes matter.
2 L at 10% + 3 L at 20%= (0.2 + 0.6) ÷ 5= 16%
Combine amounts, not percentages.
25% → 90°angle = % × 3.6total 360°
Each percent is 3.6°.

You need

  • a calculator
  • a small data set (heights, marks)
  • paper for pie charts

Tonight’s 30 minutes

  1. 8 seniors average 165.5 cm, 3 juniors 149.3 cm. Why isn’t the group average (165.5 + 149.3) ÷ 2?
  2. Find the weighted average: (8 × 165.5 + 3 × 149.3) ÷ 11 ≈ 161.1 cm.
  3. Mix 2 L of 10% juice with 3 L of 20% juice: what percent is the mixture? (16%)
  4. Draw a pie chart of a family’s monthly spending.

Words to use

  • average
  • weighted average
  • weight
  • percentage
  • pie chart
  • combine

Watch for

  • Averaging averages of unequal groups. Weight each average by its group size.
  • Adding percentages of different totals. Convert to actual amounts first, then combine.

What it sounds like at home

A short example of the conversation. Your words will differ; the questions are what matter.

YouIs the class average just the average of two sections’ averages?

Your childOnly if the sections are the same size.

A game for this week: Mixture maths

  1. Mix different amounts of sugar water (or pretend).
  2. Predict the combined concentration.
  3. Calculate the weighted average.
  4. Check predictions.

A 5-day plan, 30 minutes a day

  1. Day 1Why average of averages fails.
  2. Day 2Weighted averages.
  3. Day 3Combining percentages.
  4. Day 4Pie charts.
  5. Day 5Mixture maths.

Everyday moments to practise

  • Exam grade weightings.
  • Mixing solutions.
  • Cricket averages across seasons.
  • Budget pie charts.

Quick check

Ask these at the end of the week. Tap to see the answer.

Weighted average height in the example?

About 161.1 cm.

2 L at 10% + 3 L at 20%?

16%.

Angle for 25% in a pie chart?

90°.

Ready for the next chapter when your child…

  • Computes weighted averages.
  • Combines percentages correctly.
  • Draws and reads pie charts.

Activities, wording and illustrations are Mathify Kids’ own, following the topics of NCERT’s Ganita Manjari (Class 9). See the full Class 9 parent guide for every chapter.

Questions parents ask

What is a weighted average?

An average where each value counts according to its weight, like group size.

When is a simple average of averages correct?

Only when the groups are the same size.

How do I draw a pie chart?

Each part’s angle = (part ÷ total) × 360°.