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If your older sibling's Class 9 notes are full of histograms and frequency polygons, they will not match your book. The 2026-27 Class 9 statistics chapter is new, and it asks two different questions: how do quantities of different sizes combine into one average, and how do you read a chart that shows parts of a whole? This post explains both with worked examples and checked numbers, lists the traps, and gives a practice plan.
What is in the new Class 9 statistics chapter?
The CBSE Mathematics curriculum for Class IX (2026-27) gives Statistics and Probability 10 of the 80 marks. Under Statistics it lists computing and applying a weighted average, reading stacked bar graphs and 100% stacked bar graphs, and interpreting mean, median and mode to make decisions. The NCERT chapter is Chapter 10, How Quantities Combine: Understanding Data, in Ganita Manjari, Part II. We searched the chapter for histograms and frequency polygons and found neither. Check the current year's curriculum with your school, because schools on other boards may still teach the older topics.
Why can't you just average two averages?
Example. Section A has 40 students with an average of 68 marks. Section B has 20 students with an average of 80. What is the average of all 60 students?
The tempting answer is (68 + 80) / 2 = 74. It is wrong, because it gives the 20 students in B the same say as the 40 in A.
The right way is to rebuild the totals:
Total for A = 40 × 68 = 2720. Total for B = 20 × 80 = 1600.
Combined average = (2720 + 1600) / 60 = 4320 / 60 = 72.
The answer is closer to 68 because there are more students in A. NCERT makes the same point with a badminton group of 8 seniors and 3 juniors, and shows that the simple average of averages works only when the groups are the same size, as with 5 cycling days in each of 3 weeks.
What is a weighted average?
The general formula is: weighted mean = (w₁x₁ + w₂x₂ + … + wₙxₙ) / (w₁ + w₂ + … + wₙ), where each value x is multiplied by its weight w. The chapter notes that Brahmagupta wrote this formula in the Brāhmasphuṭasiddhānta (c. 628 CE) to find the mean depth of an uneven pit.
Example (marks). A school combines internal tests, a project and the final exam in the ratio 2 : 3 : 5. Priya scores 70, 85 and 62.
Weighted score = (70 × 2 + 85 × 3 + 62 × 5) / (2 + 3 + 5) = (140 + 255 + 310) / 10 = 705 / 10 = 70.5.
The simple average would be 217 / 3 ≈ 72.3. The final exam has the largest weight, so her lower score there pulls the result down.
Example (mixture). You mix 300 mL of a drink with 4% sugar and 200 mL with 9% sugar. Sugar = 300 × 0.04 + 200 × 0.09 = 12 + 18 = 30 mL in 500 mL, so the mixture is 30/500 = 6% sugar. It is closer to 4% because there is more of that drink.
How do you read stacked and 100% stacked bar charts?
A stacked bar puts the parts of a total end to end, so the bar's full length is the total. A 100% stacked bar stretches every bar to the same length and shows each part as a percentage, a bit like a pie chart laid flat.
Example. Two schools record how students come to school.
School P: 120 walk, 240 by bus, 40 by car. Total 400.
School Q: 90 walk, 60 by bus, 50 by car. Total 200.
As percentages, P is 30% walk, 60% bus, 10% car. Q is 45% walk, 30% bus, 25% car.
On a 100% stacked bar chart, Q's walking segment is longer. That tells you a larger share of Q's students walk. It does not tell you that more students walk at Q. In fact more walk at P, 120 against 90, because P is twice the size. NCERT works through the same trap with two gardens and shows that the same 100% bar can come from very different totals. Its summary rule is worth learning: from a stacked bar chart you can always draw the 100% version, but not the other way round.
What mistakes cost marks here?
Averaging averages when the groups have different sizes.
Forgetting to divide by the sum of the weights, not by the number of values.
Mixing marks out of different totals. Turn 35 out of 50 and 44 out of 60 into percentages before you weight them.
Reading a 100% bar as a count. It shows shares only.
Comparing segments that do not start at the same point. On stacked bars, only the first segment starts at zero, so compare middle segments by their lengths, not where they end.
A practice plan for this chapter
Testing yourself is more useful than rereading: in Roediger and Karpicke's experiments, students who took recall tests remembered more a week later than students who restudied, even though restudying made them feel more confident.
Day 1: From memory, write the weighted mean formula and one example of when a simple average of averages fails. Check against the book.
Day 2: Do three problems from Exercise Sets 10.1 to 10.3: one combined average, one mixture, one weighted marks.
Day 3: Take your family's or your own weekly spending, draw it as a stacked bar and as a 100% stacked bar, and write two statements each chart can and cannot support.
Day 6: Redo anything you got wrong, without notes.
If the idea of weights is the sticking point, go back to the concept itself. The Fermi Concept Library covers every concept in mathematics with its own lesson. In Class 10 you move on to grouped data, which our guide to statistics in Class 10 covers.
Start with the badminton example in Section 10.1: cover the solution and work out why the first method fails.
