TEACHGYAN • CLASS 10 MATHEMATICS • NCERT 2026–27
Chapter 13: Statistics
Detailed Notes • Worked Examples • Competency • Board Practice
📖 Chapter Explanation
Statistics turns collected data into meaningful summaries. Students work with grouped data, measures of central tendency and graphical interpretation, while recognising that a statistic is meaningful only when the data and method are understood.
🧭 Concept Journey
📌 Core Concepts
For grouped data, the mean can be estimated using class marks and frequencies. The median identifies the central position after ordering data; the mode identifies the most frequent value/class.
💡 Worked Example
Changing one extreme value can strongly affect the mean while leaving the median less affected. This is why more than one measure may be useful.
🔍 Why the Method Works
For grouped data, the mean can be estimated using class marks and frequencies. The median identifies the central position after ordering data; the mode identifies the most frequent value/class.
⚠️ Common Errors
Do not treat a class interval’s boundary as an individual observation. Also distinguish frequency from cumulative frequency.
🧠 Concept-Based MCQs
- The mode is the value/class that is: A) smallest B) largest C) most frequent D) average
- The median is based on: A) central position B) largest value only C) product of values D) range only
- An extreme outlier generally affects the: A) mean strongly B) median always equally C) class width only D) mode always
Answer Key: 1-C, 2-A, 3-A.
📊 Case-Based / Competency
A school compares test scores from two sections. Students calculate suitable measures, identify which measure best represents the typical score and justify their choice.
- Identify the information and variables.
- Select the appropriate mathematical model.
- Calculate step by step.
- Interpret and verify the result.
🔎 Extension Case
A school analyses marks from two classes. Students use a frequency table to compare typical performance, identify the effect of an unusually high mark and explain why the mean alone may not tell the whole story.
🔥 HOTS & Board Challenge
- Explain why the selected formula or method is appropriate.
- Create a similar problem and solve it.
- Find and correct a plausible incorrect solution.
- Apply the concept in a new context.
✍️ Exam Practice
- Define the central concept.
- Solve a direct application problem.
- Solve a multi-step competency problem.
- Interpret a diagram/table/context.
- Write a complete 5-mark solution with reasoning.
📄 Practice Worksheet
- 5 concept checks
- 5 standard problems
- 3 applications
- 2 case-based questions
- 2 HOTS questions
- 1 board-style challenge
🎯 One-Minute Revision
raw data → grouping → frequency table → mean/median/mode → interpretation → comparison
🏆 Mastery Checklist
- ☐ I understand the concept.
- ☐ I can select the correct method.
- ☐ I can solve step by step.
- ☐ I can handle competency questions.
- ☐ I can verify and interpret my answer.
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Original explanatory study material aligned to NCERT/CBSE topics; textbook passages are not reproduced verbatim.