NCERT Solutions Class 9 Maths Chapter 10 — How Quantities Combine: Understanding Data#

Chapter 10 (Ganita Manjari Part II) shows how to combine data: finding the combined average of groups of different sizes, the weighted mean when parts have different importance, and the concentration of mixtures. It also covers reading and drawing stacked and 100% stacked bar charts.

exercise set 10.1 exercise set 10.2 exercise set 10.3 exercise set 10.4 exercise set 10.5 end-of-chapter exercises

Exercises#

  • Exercise Set 10.1 — Combined averages, mixtures of fertiliser, gold purity in varṇa, spice concentration (5 questions)
  • Exercise Set 10.2 — Weighted scores with given ratios (1 question)
  • Exercise Set 10.3 — Profit percentage, mixtures and dilution, ratings, langur weights, Dead Sea salinity (8 questions)
  • Exercise Set 10.4 — Reading and drawing stacked bar charts (2 questions)
  • Exercise Set 10.5 — 100% stacked bar chart of daily activity (1 question)
  • End-of-Chapter Exercises — Run rates, shares, average prices, reading charts, projects (14 questions)

What you will learn#

  • Combining averages of groups of different sizes: the combined and weighted mean.
  • Mixtures and concentrations — fertilisers, purity of gold, salinity.
  • Reading and drawing stacked and 100% stacked bar charts.

Key formulas and results#

  • Combined mean of two groups: $\dfrac{n_1\bar{x}_1 + n_2\bar{x}_2}{n_1 + n_2}$.
  • Weighted mean: $\dfrac{\sum w_i x_i}{\sum w_i}$.

Read and revise#

Frequently asked questions#

How many exercises are in Class 9 Maths Chapter 10?
Five exercise sets — 10.1 (5 questions), 10.2 (1 question), 10.3 (8 questions), 10.4 (2 questions) and 10.5 (1 question) — plus 14 end-of-chapter exercises. Every question is solved step by step here.
Why can't you just average two averages?
Because the groups may be different sizes. A class of 40 should count more than a class of 10, so each average is weighted by the size of its group.

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