Chapter 8 of 8

100%

Tamil Nadu (TNBSE)Class 10 Mathematics★ 8-12 marks in the TN SSLC Class 10 Maths public exam through MCQs, standard-deviation and probability problems

Statistics and Probability

Samacheer Kalvi (TN State Board) Class 10 Maths Chapter 8, Statistics and Probability. Measures of dispersion (range, variance, standard deviation, coefficient of variation) and probability (concept, types of events, the addition theorem). Notes with formulas, worked examples, common mistakes, book-back practice and quick revision.

⏱ 20 min readMedium difficulty✓ Free · NCERT-aligned

Worksheet

Podcast

Listen as a conversation

A teacher & a student talk through the chapter — in your language.

Mind Map

The chapter at a glance

Every concept and exam-favourite branch — revisable in 5 minutes.

…

Study Guide

Night-before notes

Key points, glossary and the questions most likely to show up.

…

VocabularyBuild your vocabularyLexiGenome mines the key words and schedules them with spaced repetition.Mine words →

By the end of this chapter you'll be able to…

1Find the range, variance and standard deviation
2Compute and interpret the coefficient of variation
3State and apply the definition of probability
4Use complementary and mutually exclusive events
5Apply the addition theorem of probability

💡

Why this chapter matters

Statistics and Probability is a high-scoring final chapter. Standard deviation, coefficient of variation and probability problems are formula-driven and dependable for marks in the TN SSLC exam.

Before you start — revise these

A 5-minute refresher here will save you 30 minutes of confusion below.

🔗

Class 9 — Statistics

Mean and basic data handling.

Statistics and Probability — Class 10 Maths (Samacheer Kalvi)

TN State Board (Samacheer Kalvi) Class 10 Mathematics, Chapter 8 (the final chapter). Spread of data and the chance of events.

1. About this chapter

This chapter has two parts: measures of dispersion (how spread out data is) and probability (the chance of an event).

2. Measures of dispersion

Range = largest value − smallest value.
Variance = mean of the squared deviations: σ² = Σ(x − x̄)² / n.
Standard deviation = σ = √(Σ(x − x̄)² / n).
Coefficient of variation (CV) = (σ / x̄) × 100% — compares the consistency of two data sets (smaller CV = more consistent).

3. Probability

Probability of an event A: P(A) = (number of favourable outcomes) / (total outcomes), with 0 ≤ P(A) ≤ 1.
Complement: P(A′) = 1 − P(A).
Types of events: sure (P = 1), impossible (P = 0), mutually exclusive, complementary.
Addition theorem: P(A ∪ B) = P(A) + P(B) − P(A ∩ B); for mutually exclusive events, P(A ∩ B) = 0.

4. Worked examples

Example 1. Find the range of 12, 7, 20, 5, 15. Range = 20 − 5 = 15.

Example 2. A die is rolled. Find P(getting an even number). Favourable = {2, 4, 6} = 3; total = 6 → P = 3/6 = ½.

Example 3. If P(A) = 0.3 and P(B) = 0.5 with A, B mutually exclusive, find P(A ∪ B). P(A ∪ B) = 0.3 + 0.5 − 0 = 0.8.

5. Common mistakes

Mistake: Forgetting the square root for standard deviation. Fix: Variance = σ²; standard deviation = √variance.
Mistake: Writing P(A) > 1. Fix: Probability lies between 0 and 1.
Mistake: Ignoring P(A ∩ B) in the addition theorem. Fix: Subtract P(A ∩ B) unless the events are mutually exclusive.

6. Practice (book-back style)

Define the coefficient of variation and state its use.
Find the range of 8, 3, 11, 6, 14.
A card is drawn from a pack of 52. Find P(getting a king).
State the addition theorem of probability.
If P(A) = 0.6, find P(A′).

7. Answer key

CV = (σ/x̄) × 100%; it compares the consistency of two data sets (smaller CV = more consistent).
Range = 14 − 3 = 11.
Kings = 4; P = 4/52 = 1/13.
P(A ∪ B) = P(A) + P(B) − P(A ∩ B).
P(A′) = 1 − 0.6 = 0.4.

8. Quick revision

Chapter 8 (final) · dispersion and probability.
Range = max − min; σ = √(Σ(x − x̄)²/n); CV = (σ/x̄)×100%.
P(A) = favourable/total, 0 ≤ P(A) ≤ 1; P(A′) = 1 − P(A).
Addition theorem: P(A∪B) = P(A) + P(B) − P(A∩B).
Mutually exclusive ⇒ P(A∩B) = 0; smaller CV = more consistent.

Key formulas & results

Everything you need to memorise, in one card. Screenshot this for revision.

Standard deviation

σ = √(Σ(x − x̄)² / n)

Variance σ² is its square.

Coefficient of variation

CV = (σ / x̄) × 100%

Smaller CV = more consistent.

Probability

P(A) = favourable / total

0 ≤ P(A) ≤ 1; P(A′) = 1 − P(A).

Addition theorem

P(A ∪ B) = P(A) + P(B) − P(A ∩ B)

P(A ∩ B) = 0 if mutually exclusive.

⚠️

Common mistakes & fixes

These are the exact errors that cost students marks in board exams. Read them once, save yourself the trouble.

WATCH OUT

✗ Forgetting the square root for standard deviation

✓ Variance = σ²; standard deviation = √variance.

WATCH OUT

✗ Writing P(A) > 1

✓ Probability always lies between 0 and 1.

WATCH OUT

✗ Ignoring P(A ∩ B) in the addition theorem

✓ Subtract P(A ∩ B) unless the events are mutually exclusive.

NCERT exercises (with solutions)

Every NCERT exercise from this chapter — what it covers and how many questions to expect.

Multiple choice questions

MCQs on dispersion and probability.

Questions

Standard deviation problems

Variance, standard deviation and coefficient of variation.

Questions

Probability problems

Single events and the addition theorem.

Questions

Practice problems

Try each one yourself before tapping "Show solution". Active recall > rereading.

Q1EASY· Concept

Define the coefficient of variation and state its use.

▶ Show solution

CV = (σ/x̄) × 100%; it compares the consistency of two data sets — the smaller CV is more consistent.

Q2EASY· Numerical

Find the range of 8, 3, 11, 6, 14.

▶ Show solution

Range = 14 − 3 = 11.

Q3EASY· Numerical

A card is drawn from a pack of 52. Find P(getting a king).

▶ Show solution

Kings = 4; P = 4/52 = 1/13.

Q4EASY· Concept

State the addition theorem of probability.

▶ Show solution

P(A ∪ B) = P(A) + P(B) − P(A ∩ B).

Q5MEDIUM· Numerical

If P(A) = 0.3, P(B) = 0.5 and A, B are mutually exclusive, find P(A ∪ B).

▶ Show solution

P(A ∪ B) = 0.3 + 0.5 − 0 = 0.8.

Q6EASY· Numerical

If P(A) = 0.6, find P(A′).

▶ Show solution

P(A′) = 1 − 0.6 = 0.4.

5-minute revision

The whole chapter, distilled. Read this the night before the exam.

•Chapter 8 (final) of Samacheer Kalvi Class 10 Mathematics.
•Range = max − min; σ = √(Σ(x − x̄)²/n); variance = σ².
•CV = (σ/x̄) × 100%; smaller CV = more consistent.
•P(A) = favourable/total; 0 ≤ P(A) ≤ 1; P(A′) = 1 − P(A).
•Addition theorem: P(A∪B) = P(A) + P(B) − P(A∩B).
•Mutually exclusive ⇒ P(A∩B) = 0.

Tamil Nadu (TNBSE) marks blueprint

Where the marks come from in this chapter — so you can plan your prep.

Typical chapter weightage: 8-12 marks across MCQ, dispersion and probability problems

Question type	Marks each	Typical count	What it tests
MCQ	1	1-2	Dispersion and probability facts
Standard Deviation	2-5	1	Variance, SD, coefficient of variation
Probability	2-5	1-2	Events and addition theorem

Prep strategy

Memorise SD and CV formulas
Practise standard-deviation calculations
Learn the probability definition and limits
Apply the addition theorem carefully

Where this shows up in the real world

This chapter isn't just an exam topic — it lives in the world around you.

Quality control

Standard deviation measures consistency in manufacturing.

Risk and insurance

Probability underlies insurance and forecasting.

Sports and surveys

Statistics summarise performance and opinion data.

Exam strategy

Battle-tested tips from teachers and toppers for this chapter.

Take the square root for standard deviation
Keep probabilities between 0 and 1
Subtract P(A ∩ B) in the addition theorem
State formulas before substituting

Going beyond the textbook

For olympiad aspirants and curious learners — topics that build on this chapter.

Show how adding a constant to all data leaves the standard deviation unchanged.
Use the addition theorem for three events.

Where else this chapter is tested

CBSE board isn't the only one — other exams test this chapter too.

TN SSLC Class 10 Public ExamHigh

Foundation / NTSE MathematicsMedium

School unit testsHigh

AI helpers for this chapter

Generate more practice on the fly, or have the chapter explained at a different level.

⚡

Generate 5 more questions

Fresh MCQs + short-answer items based on this chapter, plus answer keys.

🧠

Explain at a different level

Re-explain the chapter at the level you actually want.

📝 My notes

Saved on this device — sign in to sync · how this works

0/600

Questions students ask

The real ones — pulled from the Q&A community and tutor sessions.

Standard deviation depends on the units and size of the data, while the coefficient of variation is a percentage that lets us compare the consistency of different data sets fairly.

Events that cannot happen at the same time, so their intersection is empty and P(A ∩ B) = 0.

Practice more, ask doubts, find a tutor

Tamil Nadu (TNBSE) Class 10 mock tests

Tamil Nadu (TNBSE) Class 10 PYQs

Ask in Q&A

Mathematics flashcards

Related chapters

Students who read Statistics and Probability usually read these next.

Relations and Functions

Samacheer Kalvi (TN State Board) Class 10 Maths Chapter 1, Relations and Functions. Ordered pairs and the Cartesian product, relations, functions and their types (one-one, onto, bijective), representation of functions, and composition of functions. Notes with formulas, worked examples, common mistakes, book-back practice and quick revision.

Numbers and Sequences

Samacheer Kalvi (TN State Board) Class 10 Maths Chapter 2, Numbers and Sequences. Euclid's division lemma and algorithm, the fundamental theorem of arithmetic, modular arithmetic, arithmetic and geometric progressions with their sums, and special series. Notes with formulas, worked examples, common mistakes, book-back practice and quick revision.

Algebra

Samacheer Kalvi (TN State Board) Class 10 Maths Chapter 3, Algebra. Simultaneous linear equations in three variables, GCD and LCM of polynomials, rational expressions, square root of polynomials, quadratic equations (solving, discriminant, roots) and matrices. Notes with formulas, worked examples, common mistakes, book-back practice and quick revision.

Geometry

Samacheer Kalvi (TN State Board) Class 10 Maths Chapter 4, Geometry. Similarity of triangles, the Basic Proportionality (Thales) theorem and the angle bisector theorem, the Pythagoras theorem and its converse, the concurrency theorems (Ceva and Menelaus), and tangents and secants of circles. Notes with theorems, worked examples, common mistakes, book-back practice and quick revision.

🧑‍🏫