NCERT Class 8 Mathematics Ganita Prakash Part-II: Chapter 5 — Tales by Dots and Lines
This chapter, 'Tales by Dots and Lines,' revisits the concepts of mean and median from the previous year, focusing on understanding the mean from a new perspective and observing its behavior with changing data. It explores the arithmetic mean as a measure of central tendency, illustrating how it represents the 'centre' of a dataset. The chapter uses dot plots to visualize that the mean is exactly halfway between two numbers and emphasizes that while the mean isn't always the midpoint of the extremes, the total distances from the mean to the data points below it are equal to the total distances to the data points above it. It also prompts students to consider if multiple such 'centres' can exist for a dataset. This chapter aims to deepen students' understanding of statistical measures and their properties, crucial for data analysis in mathematics.
Quick info
| Board | CBSE / NCERT |
|---|---|
| Class | Class 8 |
| Subject | Mathematics |
| Book | Ganita Prakash Part-II |
| Chapter | Chapter 5 — Tales by Dots and Lines |
| Language | English |
| PDF type | NCERT Textbook |
| Session | CBSE 2026 |
| Reading time | 3 minutes |
| Word count | 465 |
Learning outcomes
- Recall and apply the definitions of mean and median.
- Understand the mean as a measure of central tendency.
- Visualize the mean's position relative to data points using dot plots.
- Analyze how the mean behaves with changing data.
- Understand the property of equal total distances from the mean to data points below and above it.
Vocabulary
| Word | Meaning |
|---|---|
| Mean | The average of a set of numbers, calculated by summing all values and dividing by the number of values. |
| Median | The middle value in a dataset that has been ordered from least to greatest. |
| Arithmetic Mean | Another term for the mean, calculated as the sum of values divided by the count of values. |
| Central Tendency | A measure that represents the center or typical value of a dataset. |
| Dot Plot | A graphical display of data using dots above a number line. |
| Distances | The difference between the mean and individual data points. |
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Practice questions
- What is the mean of the numbers 5, 10, and 15? Answer: The mean is (5 + 10 + 15) / 3 = 10.
- If the mean of a dataset is 20, and the data points below the mean are 10 and 15, what can you say about the data points above the mean? Answer: The sum of the distances of the data points below the mean from 20 (which is 20-10 + 20-15 = 10 + 5 = 15) must be equal to the sum of the distances of the data points above the mean from 20.
- Is the mean always the midpoint of the two extreme values in a dataset? Answer: No, the mean is not always the midpoint of the two extreme values.
- How is the median defined? Answer: The median is the middle value when the data is sorted.
Frequently asked questions
What is the mean of a dataset?
The mean is the sum of all values divided by the number of values in the data.
What is the median?
The median is the middle value when the data is sorted.
How does the mean represent the 'centre' of data?
The mean represents the centre such that the total distances to the values lower than it are equal to the total distances to the values higher than it.
Is the mean always the midpoint of the extremes of the data?
No, the mean is not always the midpoint of the extremes; instead, the total distances on both sides of the mean are equal.
What is a dot plot used for in this chapter?
Dot plots are used to visualize data and illustrate the position of the mean relative to the data points.
Can there be more than one value where the sum of distances is equal on both sides?
The chapter suggests exploring this, but implies that for a given dataset, the mean is typically the unique value satisfying this property.
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Topics covered
NCERT Class 8 Mathematics — Ganita Prakash Part-II — Chapter 5 — Tales by Dots and Lines. Verified by NCERT Help Editorial Team. Reviewed on 29 Jul 2026. Last updated 10 Aug 2026.