NCERT Class 11 Mathematics Mathematics: Chapter 13 — Statistics
This chapter, Statistics, from NCERT Class 11 Mathematics, introduces the concept of dispersion as a crucial aspect of data analysis beyond central tendency. It highlights that while measures like mean and median provide a central value, they don't fully describe the data's spread. The chapter uses an example of two batsmen's scores to illustrate how variability differs even when central measures are the same. It explains that dispersion measures how data points are scattered around the central value. The text defines mean and median calculation methods and introduces the idea of a single number, a 'measure of dispersion', to quantify this spread. This chapter aims to equip students with tools to understand and calculate these important measures of dispersion for both ungrouped and grouped data, enhancing their ability to interpret data effectively for CBSE learning.
Quick info
| Board | CBSE / NCERT |
|---|---|
| Class | Class 11 |
| Subject | Mathematics |
| Book | Mathematics |
| Chapter | Chapter 13 — Statistics |
| Language | English |
| PDF type | NCERT Textbook |
| Session | CBSE 2026 |
| Reading time | 3 minutes |
| Word count | 548 |
Learning outcomes
- Understand the limitations of measures of central tendency.
- Recognize the importance of data variability or dispersion.
- Define and understand the concept of a measure of dispersion.
- Learn methods for calculating measures of dispersion for ungrouped and grouped data.
Vocabulary
| Word | Meaning |
|---|---|
| Statistics | The science of collecting, analyzing, interpreting, and presenting data. |
| Data | Facts and statistics collected together for reference or analysis. |
| Measure of Central Tendency | A value that represents the center or typical value of a dataset (e.g., mean, median, mode). |
| Arithmetic Mean | The sum of observations divided by the number of observations. |
| Median | The middle value in a dataset when arranged in order. |
| Variability | The extent to which data points differ from each other or from the mean. |
| Measure of Dispersion | A single number that describes the spread or scatter of a dataset. |
| Ungrouped Data | Data that is listed individually. |
| Grouped Data | Data that is organized into frequency tables or classes. |
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Practice questions
- Why are measures of central tendency not sufficient to give complete information about a given data? Answer: Measures of central tendency do not provide information about how the data points are scattered or spread out.
- What is the purpose of studying variability in statistics? Answer: Variability is studied to understand the spread or dispersion of data points around a measure of central tendency.
- Define a 'measure of dispersion'. Answer: A measure of dispersion is a single number that quantifies the spread or scatter of data points in a dataset.
- What are the two types of data mentioned for calculating measures of dispersion? Answer: The two types are ungrouped data and grouped data.
Practice MCQs
Q1. Which of the following is NOT a measure of central tendency mentioned in the text?
Explanation: Range is a measure of dispersion, not central tendency. Mean, median, and mode are measures of central tendency.
Q2. The text uses an example of two batsmen. What was the key difference highlighted between their scores?
Explanation: Although both batsmen had the same mean and median (53), Batsman A's scores ranged from 0 to 117, indicating greater variability than Batsman B's scores (46 to 60).
Q3. What does a measure of dispersion aim to describe?
Explanation: Measures of dispersion quantify how spread out or bunched together the data points are around a measure of central tendency.
Q4. According to the text, what is Karl Pearson known for in statistics?
Explanation: While the text doesn't explicitly state Karl Pearson's contributions in detail, he is famously associated with developing key measures of dispersion like the standard deviation and coefficient of variation.
Q5. If two datasets have the same mean, what additional information is needed for better interpretation?
Explanation: The text emphasizes that measures of central tendency alone are insufficient; understanding the variability or dispersion is crucial for a complete interpretation of data.
Frequently asked questions
What is statistics?
Statistics is the science that deals with data collected for specific purposes, involving methods of analysis, interpretation, and decision-making.
What are measures of central tendency?
Measures of central tendency are representative values that indicate the center or typical value of a dataset, such as the arithmetic mean, median, and mode.
Why is variability important in statistics?
Variability, or dispersion, is important because it shows how spread out or clustered the data points are around the central tendency, providing a more complete picture of the data.
What is a measure of dispersion?
A measure of dispersion is a single numerical value used to describe the extent of scatter or spread in a dataset.
What is the difference between ungrouped and grouped data in the context of dispersion?
Ungrouped data consists of individual observations, while grouped data is organized into classes or frequency tables. Different methods are used to calculate dispersion for each type.
Can the mean and median alone determine if two datasets have similar performance?
No, the mean and median alone are not sufficient. The variability or spread of the data must also be considered for a complete comparison.
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NCERT Class 11 Mathematics — Mathematics — Chapter 13 — Statistics. Verified by NCERT Help Editorial Team. Reviewed on 29 Jul 2026. Last updated 10 Aug 2026.