Chapter 8 of 9

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Tamil Nadu (TNBSE)Class 9 Mathematics★ 5-8 marks in the TN Class 9 annual exam through MCQs and central-tendency problems

Statistics

Samacheer Kalvi (TN State Board) Class 9 Maths Chapter 8, Statistics. Measures of central tendency — arithmetic mean, median and mode — for ungrouped and grouped data, with their relationship. Notes with formulas, worked examples, common mistakes, book-back practice and quick revision.

⏱ 16 min readEasy difficulty✓ Free · NCERT-aligned

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

1Compute the arithmetic mean for ungrouped and grouped data
2Find the median of a data set
3Find the mode of a data set
4Apply the empirical relation among the measures
5Interpret central-tendency results

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Why this chapter matters

Statistics teaches how to summarise data using the mean, median and mode. These are easy, formula-driven, reliable marks in the TN Class 9 exam and the basis for Class 10 statistics.

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Class 8 — Data handling

Tables, averages and frequency.

Statistics — Class 9 Maths (Samacheer Kalvi)

TN State Board (Samacheer Kalvi) Class 9 Mathematics, Chapter 8. Summarising data with the mean, median and mode.

1. About this chapter

This chapter covers the three measures of central tendency — mean, median and mode — for ungrouped and grouped data, and the relation between them.

2. Mean, median and mode

Arithmetic mean (ungrouped): x̄ = Σx / n; (grouped): x̄ = Σfx / Σf.
Median: the middle value when data is arranged in order.
- For n odd, median = the ((n+1)/2)ᵗʰ value; for n even, the average of the two middle values.
Mode: the value that occurs most often.

3. Relationship

An empirical relation among the measures: Mode = 3 Median − 2 Mean.

4. Worked examples

Example 1. Find the mean of 4, 8, 6, 10, 12. x̄ = (4 + 8 + 6 + 10 + 12)/5 = 40/5 = 8.

Example 2. Find the median of 7, 3, 9, 5, 11. In order: 3, 5, 7, 9, 11 → middle value = 7.

Example 3. Find the mode of 2, 3, 3, 5, 7, 3, 8. 3 occurs most often → mode = 3.

5. Common mistakes

Mistake: Finding the median without ordering the data. Fix: Arrange the values in ascending order first.
Mistake: Dividing by the wrong count for grouped mean. Fix: Use x̄ = Σfx / Σf.
Mistake: Confusing mode with mean. Fix: Mode = most frequent value; mean = average.

6. Practice (book-back style)

Find the mean of 5, 10, 15, 20.
Find the median of 2, 8, 4, 6.
Find the mode of 4, 4, 6, 9, 4, 6.
Write the empirical relation between mean, median and mode.
Write the grouped-data mean formula.

7. Answer key

(5 + 10 + 15 + 20)/4 = 50/4 = 12.5.
In order 2, 4, 6, 8 → median = (4 + 6)/2 = 5.
4 occurs most → mode = 4.
Mode = 3 Median − 2 Mean.
x̄ = Σfx / Σf.

8. Quick revision

Chapter 8 · mean, median, mode.
Mean x̄ = Σx/n (ungrouped) or Σfx/Σf (grouped).
Median = middle value (order data first; average two middles if n even).
Mode = most frequent value.
Empirical relation: Mode = 3 Median − 2 Mean.

Key formulas & results

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

Mean

x̄ = Σx/n (ungrouped); x̄ = Σfx/Σf (grouped)

The arithmetic average.

Median

middle value of ordered data

Average two middles if n is even.

Mode

most frequently occurring value

Data may have more than one mode.

Empirical relation

Mode = 3 Median − 2 Mean

Approximate link among the three.

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Common mistakes & fixes

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

WATCH OUT

✗ Finding the median without ordering the data

✓ Arrange the values in ascending order first.

WATCH OUT

✗ Dividing by the wrong count for grouped mean

✓ Use x̄ = Σfx / Σf.

WATCH OUT

✗ Confusing mode with mean

✓ Mode is the most frequent value; mean is the average.

NCERT exercises (with solutions)

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

Multiple choice questions

MCQs on mean, median and mode.

Questions

Central tendency problems

Compute mean, median and mode.

Questions

Grouped data

Mean of grouped frequency distributions.

Questions

Practice problems

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

Q1EASY· Numerical

Find the mean of 5, 10, 15, 20.

▶ Show solution

(5 + 10 + 15 + 20)/4 = 12.5.

Q2EASY· Numerical

Find the median of 2, 8, 4, 6.

▶ Show solution

Ordered: 2, 4, 6, 8 → median = (4 + 6)/2 = 5.

Q3EASY· Numerical

Find the mode of 4, 4, 6, 9, 4, 6.

▶ Show solution

4 occurs most often → mode = 4.

Q4EASY· Recall

Write the empirical relation between mean, median and mode.

▶ Show solution

Mode = 3 Median − 2 Mean.

Q5EASY· Recall

Write the grouped-data mean formula.

▶ Show solution

x̄ = Σfx / Σf.

Q6EASY· Numerical

Find the mean of 4, 8, 6, 10, 12.

▶ Show solution

40/5 = 8.

5-minute revision

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

•Chapter 8 of Samacheer Kalvi Class 9 Mathematics.
•Mean x̄ = Σx/n (ungrouped) or Σfx/Σf (grouped).
•Median = middle value (order first; average two middles if n even).
•Mode = most frequent value.
•Empirical relation: Mode = 3 Median − 2 Mean.
•Choose the right measure for the data.

Tamil Nadu (TNBSE) marks blueprint

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

Typical chapter weightage: 5-8 marks across MCQ and central-tendency problems

Question type	Marks each	Typical count	What it tests
MCQ	1	1-2	Definitions and formulas
Short Answer	2-3	1-2	Mean, median, mode
Grouped Data	2-3	1	Mean of a distribution

Prep strategy

Order data before finding the median
Use Σfx/Σf for grouped mean
Identify the most frequent value for mode
Learn the empirical relation

Where this shows up in the real world

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

Surveys

Averages summarise marks, incomes and opinions.

Sports

Mean and median describe player performance.

Economics

Central tendency summarises prices and wages.

Exam strategy

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

Always order data for the median
Use the correct mean formula
State the mode as the most frequent value
Apply the empirical relation when two measures are given

Going beyond the textbook

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

Find the missing value given the mean of a data set.
Show how an outlier shifts the mean but not the median.

Where else this chapter is tested

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

TN Class 9 Annual ExamHigh

Foundation / NTSE MathematicsMedium

School unit testsHigh

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Questions students ask

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

When the data has extreme values (outliers), the median better represents the centre because it is not affected by very large or small values.

Yes — if two or more values occur with the same highest frequency, the data is bimodal or multimodal.

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