NCERT Class 10 Mathematics Mathematics: Chapter 13 — 1 Introduction
This chapter, Statistics, builds upon the concepts introduced in Class IX regarding data classification and representation. It extends the study of measures of central tendency – mean, median, and mode – from ungrouped to grouped data. The chapter details the formula for calculating the mean of grouped data using frequencies and observations (xi, fi). It provides an example demonstrating how to calculate the mean marks obtained by students by summing the products of marks and their frequencies, and then dividing by the total number of students. The chapter also introduces the concept of cumulative frequency, cumulative frequency distribution, and cumulative frequency curves (ogives), which are essential tools for analyzing statistical data. This chapter is crucial for students to develop a deeper understanding of statistical analysis and its applications in various fields, aligning with the CBSE curriculum.
Quick info
| Board | CBSE / NCERT |
|---|---|
| Class | Class 10 |
| Subject | Mathematics |
| Book | Mathematics |
| Chapter | Chapter 13 — 1 Introduction |
| Language | English |
| PDF type | NCERT Textbook |
| Session | CBSE 2026 |
| Reading time | 3 minutes |
| Word count | 512 |
Learning outcomes
- Understand the concept of mean for grouped data.
- Apply the formula for calculating the mean of grouped data.
- Learn about cumulative frequency and cumulative frequency distribution.
- Understand the concept of cumulative frequency curves (ogives).
Vocabulary
| Word | Meaning |
|---|---|
| Statistics | The science of collecting, analyzing, and interpreting data. |
| Grouped frequency distribution | Data organized into classes or intervals with their corresponding frequencies. |
| Mean | The average of a set of numbers. |
| Frequency | The number of times a particular data value occurs. |
| Summation (Σ) | A mathematical notation for summing a sequence of numbers. |
| Cumulative frequency | The sum of frequencies for all data values less than or equal to a given value. |
| Ogives | Graphs representing cumulative frequency distributions. |
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Practice questions
- What is the formula for the mean of grouped data? Answer: The mean (x) of grouped data is given by x = Σ(fi xi) / Σfi, where xi are the observations and fi are their respective frequencies.
- If xi represents the marks and fi represents the number of students, what does Σ(fi xi) represent? Answer: Σ(fi xi) represents the sum of the products of marks obtained by each student and the number of students who obtained those marks, effectively the total marks obtained by all students.
- What is the total number of observations in Example 1? Answer: The total number of observations (students) in Example 1 is 30, which is Σfi.
Frequently asked questions
What is the main focus of Chapter 13 of the NCERT Class 10 Mathematics textbook?
Chapter 13 focuses on Statistics, specifically extending the concepts of mean, median, and mode to grouped data, and introducing cumulative frequency and ogives.
How is the mean of grouped data calculated in this chapter?
The mean of grouped data is calculated using the formula x = Σ(fi xi) / Σfi, where xi are the class marks and fi are the corresponding frequencies.
What is the significance of Σfi in the mean formula?
Σfi represents the total number of observations in the dataset.
What are ogives?
Ogives are graphical representations of cumulative frequency distributions, used to find the median, quartiles, etc.
What is cumulative frequency?
Cumulative frequency is the sum of frequencies of all classes up to and including a particular class.
Related resources
Important topics
Topics covered
NCERT Class 10 Mathematics — Mathematics — Chapter 13 — 1 Introduction. Verified by NCERT Help Editorial Team. Reviewed on 29 Jul 2026. Last updated 10 Aug 2026.