Revision Notes for Class 8 Maths Chapter 12: Tales by Dots and Lines

Condensed revision notes for Class 8 Maths Chapter 12: Tales by Dots and Lines – Ganita Prakash. These Class 8 Mathematics Chapter 12 notes are ideal for quick revision just before exams.

Last Updated: September 23, 2026

• Mean (average) = sum of all values ÷ number of values.
• Mean of first n natural numbers = (n+1)/2. Mean of first n odd numbers = n.
• Median: the middle value of a sorted data set. For odd count n, it’s the ((n+1)/2)th term. For even count n, it’s the average of the (n/2)th and (n/2+1)th terms.
• Effect of adding a value: adding a value above the current mean increases the mean; below it, decreases the mean; equal to it, leaves the mean unchanged.
• Effect on median: unlike the mean, the median depends only on rank/position, not exact size — so it’s much less sensitive to outliers than the mean.
• Dot plot: a simple chart showing each data value as a dot above a number line, useful for quickly seeing spread and repeated values.
• Line graph: connects data points with straight lines, ideal for showing how a quantity changes over time.
• Combined mean of two groups = (sum of group 1 + sum of group 2) ÷ (count 1 + count 2) — NOT simply the average of the two group means unless the groups are equal size.
• Outliers (unusually large/small values) can distort the mean significantly while barely affecting the median — this is why median is often preferred for skewed real-world data like income or house prices.
• Reading graphs critically: always check what a graph actually shows (and doesn’t show) before accepting a claim based on it — a graph about lighting sources says nothing about power cuts, for example.

More on this chapter: NCERT Solutions for Class 8 Maths Chapter 12 | Extra Questions for Class 8 Maths Chapter 12 | Class 8 Maths Book | Formulas Handbook

Frequently Asked Questions

What is the purpose of plotting data as a graph rather than just listing numbers?
A graph provides a visual representation of data that makes trends, patterns, and relationships between quantities much easier to identify at a glance compared to reading through a list or table of raw numbers.

What is the difference between a linear graph and other types of graphs covered in this theme?
A linear graph represents a relationship between two quantities as a straight line, indicating the quantities change at a constant rate relative to each other, unlike curved graphs which represent changing rates.

Written by Satish

NCERTBooks.org is an independent educational resource run by a small team focused on making official NCERT textbooks easy to find, read, and download for students, parents, and teachers across India. We are not affiliated with NCERT or the Ministry of Education -- we organise publicly available NCERT content by class and subject, verify links against official sources, and build tools (like our in-browser reader) that make studying more convenient. Every guide we publish is written and reviewed by our team based on the actual NCERT curriculum and syllabus.