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Tamil Nadu (TNBSE)Class 7 Mathematics★ 6-10 marks in the TN Class 7 Term 3 exam through mean, median and mode calculations

Statistics (Term 3) - Mean, Median and Mode

Samacheer Kalvi (TN State Board) Class 7 Maths — Term 3 Chapter 5, Statistics. Organising data, the three measures of central tendency — arithmetic mean, median and mode — and how to find each, with worked examples, exercises and quick revision.

⏱ 14 min readEasy difficulty✓ Free · NCERT-aligned

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

1Organise data into a frequency distribution
2Calculate the arithmetic mean
3Find the median of ordered data
4Find the mode of a data set
5Choose an appropriate average

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Why this chapter matters

The mean, median and mode summarise data into a single representative value — a core skill in statistics used in science, sports and surveys. These averages are directly tested in the TN Class 7 Term 3 exam.

Before you start — revise these

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

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Term 1 — Number System (Integers)

Adding and dividing numbers.

Statistics (Mean, Median and Mode) — Class 7 Maths (Samacheer Kalvi)

TN State Board (Samacheer Kalvi) Class 7 Mathematics, Term 3 — Chapter 5. The three averages that represent data.

1. About this chapter

This chapter covers the organisation of data and the three measures of central tendency (averages) — the arithmetic mean, the median and the mode.

2. Data and central tendency

Data is a collection of numbers/observations; a frequency distribution records how often each value occurs.
A measure of central tendency is a single value that represents the whole data set.

3. The arithmetic mean

Mean = (sum of all observations) ÷ (number of observations).
Example: the mean of 4, 8, 6, 10, 2 = (4+8+6+10+2) ÷ 5 = 30 ÷ 5 = 6.

4. The median

The median is the middle value when the data is arranged in order.
If there are an odd number of values, it is the middle one; if even, it is the average of the two middle values.
Example: 3, 5, 7, 9, 11 → median = 7. For 4, 6, 8, 10 → median = (6 + 8)/2 = 7.

5. The mode

The mode is the value that occurs most often.
Example: in 2, 3, 3, 5, 7, 3, 8 the mode is 3 (it appears most). A data set can have more than one mode or none.

6. Worked examples

Example 1. Find the mean of 12, 15, 18, 21, 24. Sum = 90 → 90 ÷ 5 = 18.

Example 2. Find the median of 8, 3, 5, 9, 4. Arrange: 3, 4, 5, 8, 9 → middle = 5.

Example 3. Find the mode of 6, 7, 7, 8, 7, 9. 7 (occurs most often).

7. Exercises (Samacheer Kalvi)

Find the mean of 10, 20, 30, 40, 50.
The mean of 5 numbers is 12. Find their sum.
Find the median of 14, 9, 11, 6, 20.
Find the median of 2, 4, 6, 8, 10, 12.
Find the mode of 4, 5, 5, 6, 5, 7, 6.

8. Common mistakes

Mistake: Finding the median without ordering the data. Fix: Always arrange the data in order first.
Mistake: Confusing mean and mode. Fix: Mean = average (sum ÷ count); mode = most frequent value.
Mistake: Forgetting to average the two middle values for an even count. Fix: For an even number of values, median = average of the two middle values.

9. Quick revision

Term 3 · Ch 5 · statistics.
Mean = sum ÷ number of observations.
Median = middle value of ordered data (average the two middle ones if the count is even).
Mode = most frequently occurring value.

Key formulas & results

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

Mean

sum of observations ÷ number of observations

The average.

Median (odd)

the middle value of ordered data

Arrange first.

Median (even)

average of the two middle values

When count is even.

Mode

the most frequently occurring value

May be none or several.

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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

✓ Always arrange the data in order first.

WATCH OUT

✗ Confusing mean and mode

✓ Mean = average (sum ÷ count); mode = most frequent value.

WATCH OUT

✗ Forgetting to average the two middle values for an even count

✓ For an even number of values, the median is the average of the two middle values.

NCERT exercises (with solutions)

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

Mean

Find the mean; find the sum from the mean.

Questions

Median

Find the median for odd and even counts.

Questions

Mode

Find the mode of data sets.

Questions

Practice problems

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

Q1EASY· Mean

Find the mean of 10, 20, 30, 40, 50.

▶ Show solution

150 ÷ 5 = 30.

Q2MEDIUM· Mean

The mean of 5 numbers is 12. Find their sum.

▶ Show solution

Sum = mean × count = 12 × 5 = 60.

Q3EASY· Median

Find the median of 14, 9, 11, 6, 20.

▶ Show solution

Order: 6, 9, 11, 14, 20 → median 11.

Q4MEDIUM· Median

Find the median of 2, 4, 6, 8, 10, 12.

▶ Show solution

Two middle values 6 and 8 → (6 + 8)/2 = 7.

Q5EASY· Mode

Find the mode of 4, 5, 5, 6, 5, 7, 6.

▶ Show solution

5 (occurs most often).

Q6EASY· Mean

Find the mean of 12, 15, 18, 21, 24.

▶ Show solution

90 ÷ 5 = 18.

5-minute revision

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

•Term 3 Chapter 5 of Samacheer Kalvi Class 7 Maths.
•Mean = sum of observations ÷ number of observations.
•Median = the middle value of ordered data.
•For an even number of values, the median is the average of the two middle ones.
•Mode = the most frequently occurring value.
•Mean, median and mode are the three measures of central tendency.

Tamil Nadu (TNBSE) marks blueprint

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

Typical chapter weightage: 6-10 marks across the three averages

Question type	Marks each	Typical count	What it tests
Mean	1-2	2	Average and reverse mean
Median	1-2	2	Odd and even counts
Mode	1	1-2	Most frequent value

Prep strategy

Add carefully and divide by the count for the mean
Always order data before finding the median
Average the two middle values for even counts
Tally frequencies to find the mode

Where this shows up in the real world

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

Sports

Batting and run averages use the mean.

Surveys

The mode shows the most common response.

Economics

Median income represents a typical earner.

Exam strategy

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

Show the sum and count for the mean
Order the data before the median
Average two middle values for even counts
Tally to identify the mode

Going beyond the textbook

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

If the mean of 6 numbers is 10 and five of them are 8, 9, 11, 12, 7, find the sixth.
Create a data set whose mean, median and mode are all 5.

Where else this chapter is tested

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

TN Class 7 Term 3 ExamHigh

NMMS / Foundation MathsMedium

School unit testsHigh

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Questions students ask

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

The mean is the arithmetic average (sum ÷ count), the median is the middle value of ordered data, and the mode is the value that occurs most often.

Yes. If two or more values occur with the same highest frequency, the data has more than one mode; if no value repeats, it has no mode.

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