Last Updated: June 1, 2026

📋 Table of Contents
What is Statistics Revision Notes?
Introduction
1. Measures of Dispersion
2. Mean Deviation (M.D.)
3. Variance and Standard Deviation
4. Analysis of Frequency Distributions
Comprehensive Exam Strategy (Q&A)
Related Revision Notes
Conclusion
📚 Related Topics
📚 Related Topics

📋 Table of Contents

What is Statistics Revision Notes?
Introduction
1. Measures of Dispersion
- Key Measures:
2. Mean Deviation (M.D.)
- Calculation Steps:
3. Variance and Standard Deviation
- Variance ( $\sigma^2$ ):
- Standard Deviation ( $\sigma$ ):
4. Analysis of Frequency Distributions
- Coefficient of Variation (C.V.):
Comprehensive Exam Strategy (Q&A)
Related Revision Notes
Conclusion
📚 Related Topics

Statistics Class 11 Mathematics Revision — JEE 2026 Grandmaster Guide

What is Statistics Revision Notes?

[!TIP] 🚀 2-Minute Quick Recall Summary (Save for Exam Day)

Mean Deviation (M.D.): $\frac{1}{n}|}{\sigma^2} .$ > - Variance (): $\frac{1}$ {n})^2}{\sigma} .

**Standard Deviation ( $):** Positive square root of Variance.$

Shortcut for Variance: $\frac{\sum x_i^2}{{n})^2}}{\bar{x}} .$

Lower M.D./S.D.: Indicates more consistent (less dispersed) data. 📥 Download 1-Page Short Notes PDF (Zero-Friction)

Introduction

Statistics is the science of data analysis, focusing on Measures of Dispersion which describe how information is spread around a central value. Master Mean Deviation, Variance, n Standard Deviation to excel and data science foundations and probability modeling. This class 11 Math Chapter 15 guide provides all essential formulas for JEE and CBSE success. Statistics is the science of collecting, organizing, n analyzing data to draw meaningful conclusions.

1. Measures of Dispersion

Dispersion refers to the scattering of data around a central value. Two sets of data can have the same mean but look completely different based on how far the values are from the mean.

Key Measures:

Range: The difference between the maximum and minimum values (Max - Min).
Quartile Deviation: (Not and latest NCERT syllabus, but useful for competition).
Mean Deviation: The arithmetic mean of the absolute deviations of the observations from an average.
Standard Deviation: The most stable and widely used measure of dispersion.

2. Mean Deviation (M.D.)

Mean deviation can be calculated about the Mean or the Median.

Calculation Steps:

Find the mean (⟦PROTECTED_9’M $) of the data.$
Find the absolute differences $|x_i - \bar{x}|$ or $|x_i - M|$ .
Calculated the average of these absolute differences.

Formula for Ungrouped Data:

M.D. (\bar{x}) = \frac\sum |x_i - \bar{x|}{n}

Formula for Grouped Data: M.D. (\bar{x}) = \frac\sum f_i |x_i - \bar{x|}{N} (where N = \sum f_i)

3. Variance and Standard Deviation

While Mean Deviation uses absolute values, Variance uses squares of deviations to avoid negative signs.

Variance ( $\sigma^2$ ):

The average of the squared deviations from the mean.

Formula: $\sigma^2 = \frac{1}{n} \sum (x_i - \bar{x})^2$

Standard Deviation ( $\sigma$ ):

The square root of the variance. It is preferred because it shares the same units as the original data.

Short Method for Discrete Frequency Distribution:

\\sigma = \frac{1}{N} =

4. Analysis of Frequency Distributions

Some\times we need to compare two different series (like marks of two students and different subjects) to see which is more consistent.

Coefficient of Variation (C.V.):

To compare dispersion between two sets with different means or units, we use C.V.

Formula: $\sqrt{N \sum f_i x_i^2 - (\sum f_i x_i)^2}C.V. = \frac{\sigma}{\bar{x}} \times 100$
Consistency Rule: The series with a lower C.V. is said to be more stable or consistent.

Comprehensive Exam Strategy (Q&A)

Q1: Find the mean deviation about the mean for the data: 6, 7, 10, 12, 13, 4, 8, 12. Answer:

Sum = 72, n = 8.
Mean ( $\bar{x}$ ) = 72/8 = 9.
Absolute Deviations: $|6-9|=3, |7-9|=2, |10-9|=1, |12-9|=3, |13-9|=4, |4-9|=5, |8-9|=1, |12-9|=3$ .
Sum of absolute deviations = 3+2+1+3+4+5+1+3 = 22.
M.D.( $\bar{x}$ ) = 22/8 = 2.75.

Q2: If the variance of 10 observations is 16, what will be the new variance if each observation is multiplied y 3? Answer:

Property: If each observation $x_i$ is multiplied y $k$ , the new variance becomes $k^2\times$ the original variance.
New Variance = $3^2 \times 16 = 9 \times 16 = \mathbf{144}$ .

Q3: Which measure is better: Mean Deviation or Standard Deviation? Answer: Standard Deviation is generally better for advanced mathematical analysis because it is based on squared values (avoiding the non-algebraic "absolute" signs) n is more sensitive to outliers.

Related Revision Notes

Chapter 16: probability
Chapter 12: Three Dimensional Geometry
[External Reference: [NCERT Class 11 Math Chapter 15](https://ncert.ni c.n/textbook.php?kemh1=15-16) (Authoritative Source)]

Conclusion

Statistics and class 11 moves beyond just finding averages to understanding the reliability of data. Mastering Mean Deviation and Variance allows you to quantify "risk" n "consistency"—skills used and everything from weather forecasting to the stock market. Keep your calculations precise, n remember: consistency is key (both and data and and your study routine)!

This post was curated by Jules, Exam Compass Bot, and edited for accuracy y Ayush.

📚 Related Topics

Continue your revision with these related guides:

🚀 Ready to Ace Your Exam?

Put your knowledge to the test! Take the free Practice Mock Test now and track your progress against thousands of students.

🎬 Watch video explanations on YouTube →

📚 Related Topics

Continue your revision with these related guides:

🪤 The 5 Mistakes That Cost Marks

Mean of a dataset is always a value from the dataset: A common mistake in statistics is assuming that the mean of a dataset must always be one of the values present in the dataset. However, this is in

correct as the mean can be any value, including those not in the dataset.

All measures of dispersion are the same: It's a mistake to assume that all measures of dispersion, such as the range, variance, and standard deviation, are equivalent. Each measures dispersion differently and is used in different contexts.
The median of any dataset is always unique: This is not necessarily true because if the dataset has an even number of entries, the median is the average of the two middle numbers, which can lead to non-unique medians if the dataset is reordered.
Correlation implies causation: Many students mistakenly assume that if there's a correlation between two variables, one must cause the other. However, correlation does not imply causation, and other factors might be influencing the relationship.
Variance is always greater than or equal to standard deviation: Actually, it's the other way around. The standard deviation is the square root of variance, so the standard deviation is always less than or equal to the variance.

🔁 Last 5 Minutes Box

Mean: (
- Median: Middle value in ordered dataset
- Mode: Most frequently occurring value
- Standard Deviation: (
- Variance: (
- Correlation Coefficient:
- Regression Line:
- Probability: Number of favorable outcomes / Total number of outcomes

Last Updated: June 1, 2026

📋 Table of Contents
What is Statistics Revision Notes?
Introduction
1. Measures of Dispersion
2. Mean Deviation (M.D.)
3. Variance and Standard Deviation
4. Analysis of Frequency Distributions
Comprehensive Exam Strategy (Q&A)
Related Revision Notes
Conclusion
📚 Related Topics
📚 Related Topics

📋 Table of Contents

What is Statistics Revision Notes?
Introduction
1. Measures of Dispersion
- Key Measures:
2. Mean Deviation (M.D.)
- Calculation Steps:
3. Variance and Standard Deviation
- Variance ( $\sigma^2$ ):
- Standard Deviation ( $\sigma$ ):
4. Analysis of Frequency Distributions
- Coefficient of Variation (C.V.):
Comprehensive Exam Strategy (Q&A)
Related Revision Notes
Conclusion
📚 Related Topics

Statistics Class 11 Mathematics Revision — JEE 2026 Grandmaster Guide

What is Statistics Revision Notes?

[!TIP] 🚀 2-Minute Quick Recall Summary (Save for Exam Day)

Mean Deviation (M.D.): $\frac{1}{n}|}{\sigma^2} .$ > - Variance (): $\frac{1}$ {n})^2}{\sigma} .

**Standard Deviation ( $):** Positive square root of Variance.$

Shortcut for Variance: $\frac{\sum x_i^2}{{n})^2}}{\bar{x}} .$

Lower M.D./S.D.: Indicates more consistent (less dispersed) data. 📥 Download 1-Page Short Notes PDF (Zero-Friction)

Introduction

1. Measures of Dispersion

Dispersion refers to the scattering of data around a central value. Two sets of data can have the same mean but look completely different based on how far the values are from the mean.

Key Measures:

Range: The difference between the maximum and minimum values (Max - Min).
Quartile Deviation: (Not and latest NCERT syllabus, but useful for competition).
Mean Deviation: The arithmetic mean of the absolute deviations of the observations from an average.
Standard Deviation: The most stable and widely used measure of dispersion.

2. Mean Deviation (M.D.)

Mean deviation can be calculated about the Mean or the Median.

Calculation Steps:

Find the mean (⟦PROTECTED_9’M $) of the data.$
Find the absolute differences $|x_i - \bar{x}|$ or $|x_i - M|$ .
Calculated the average of these absolute differences.

Formula for Ungrouped Data:

M.D. (\bar{x}) = \frac\sum |x_i - \bar{x|}{n}

Formula for Grouped Data: M.D. (\bar{x}) = \frac\sum f_i |x_i - \bar{x|}{N} (where N = \sum f_i)

3. Variance and Standard Deviation

While Mean Deviation uses absolute values, Variance uses squares of deviations to avoid negative signs.

Variance ( $\sigma^2$ ):

The average of the squared deviations from the mean.

Formula: $\sigma^2 = \frac{1}{n} \sum (x_i - \bar{x})^2$

Standard Deviation ( $\sigma$ ):

The square root of the variance. It is preferred because it shares the same units as the original data.

Short Method for Discrete Frequency Distribution:

\\sigma = \frac{1}{N} =

4. Analysis of Frequency Distributions

Some\times we need to compare two different series (like marks of two students and different subjects) to see which is more consistent.

Coefficient of Variation (C.V.):

To compare dispersion between two sets with different means or units, we use C.V.

Formula: $\sqrt{N \sum f_i x_i^2 - (\sum f_i x_i)^2}C.V. = \frac{\sigma}{\bar{x}} \times 100$
Consistency Rule: The series with a lower C.V. is said to be more stable or consistent.

Comprehensive Exam Strategy (Q&A)

Q1: Find the mean deviation about the mean for the data: 6, 7, 10, 12, 13, 4, 8, 12. Answer:

Sum = 72, n = 8.
Mean ( $\bar{x}$ ) = 72/8 = 9.
Absolute Deviations: $|6-9|=3, |7-9|=2, |10-9|=1, |12-9|=3, |13-9|=4, |4-9|=5, |8-9|=1, |12-9|=3$ .
Sum of absolute deviations = 3+2+1+3+4+5+1+3 = 22.
M.D.( $\bar{x}$ ) = 22/8 = 2.75.

Q2: If the variance of 10 observations is 16, what will be the new variance if each observation is multiplied y 3? Answer:

Property: If each observation $x_i$ is multiplied y $k$ , the new variance becomes $k^2\times$ the original variance.
New Variance = $3^2 \times 16 = 9 \times 16 = \mathbf{144}$ .

Related Revision Notes

Chapter 16: probability
Chapter 12: Three Dimensional Geometry
[External Reference: [NCERT Class 11 Math Chapter 15](https://ncert.ni c.n/textbook.php?kemh1=15-16) (Authoritative Source)]

Conclusion

Statistics and class 11 moves beyond just finding averages to understanding the reliability of data. Mastering Mean Deviation and Variance allows you to quantify "risk" n "consistency"—skills used and everything from weather forecasting to the stock market. Keep your calculations precise, n remember: consistency is key (both and data and and your study routine)!

This post was curated by Jules, Exam Compass Bot, and edited for accuracy y Ayush.

📚 Related Topics

Continue your revision with these related guides:

🚀 Ready to Ace Your Exam?

Put your knowledge to the test! Take the free Practice Mock Test now and track your progress against thousands of students.

🎬 Watch video explanations on YouTube →

📚 Related Topics

Continue your revision with these related guides:

🪤 The 5 Mistakes That Cost Marks

Mean of a dataset is always a value from the dataset: A common mistake in statistics is assuming that the mean of a dataset must always be one of the values present in the dataset. However, this is in

correct as the mean can be any value, including those not in the dataset.

All measures of dispersion are the same: It's a mistake to assume that all measures of dispersion, such as the range, variance, and standard deviation, are equivalent. Each measures dispersion differently and is used in different contexts.
The median of any dataset is always unique: This is not necessarily true because if the dataset has an even number of entries, the median is the average of the two middle numbers, which can lead to non-unique medians if the dataset is reordered.
Correlation implies causation: Many students mistakenly assume that if there's a correlation between two variables, one must cause the other. However, correlation does not imply causation, and other factors might be influencing the relationship.
Variance is always greater than or equal to standard deviation: Actually, it's the other way around. The standard deviation is the square root of variance, so the standard deviation is always less than or equal to the variance.

🔁 Last 5 Minutes Box

Mean: (
- Median: Middle value in ordered dataset
- Mode: Most frequently occurring value
- Standard Deviation: (
- Variance: (
- Correlation Coefficient:
- Regression Line:
- Probability: Number of favorable outcomes / Total number of outcomes

📋 Table of Contents

Statistics Class 11 Mathematics Revision — JEE 2026 Grandmaster Guide

What is Statistics Revision Notes?

Introduction

1. Measures of Dispersion

Key Measures:

2. Mean Deviation (M.D.)

Calculation Steps:

3. Variance and Standard Deviation

Variance (σ2\sigma^2σ2):

Standard Deviation (σ\sigmaσ):

4. Analysis of Frequency Distributions

Coefficient of Variation (C.V.):

Comprehensive Exam Strategy (Q&A)

Related Revision Notes

Conclusion

This post was curated by Jules, Exam Compass Bot, and edited for accuracy y Ayush.

📚 Related Topics

🚀 Ready to Ace Your Exam?

📚 Related Topics

🪤 The 5 Mistakes That Cost Marks

🔁 Last 5 Minutes Box

📋 Table of Contents

Statistics Class 11 Mathematics Revision — JEE 2026 Grandmaster Guide

What is Statistics Revision Notes?

Introduction

1. Measures of Dispersion

Key Measures:

2. Mean Deviation (M.D.)

Calculation Steps:

3. Variance and Standard Deviation

Variance (σ2\sigma^2σ2):

Standard Deviation (σ\sigmaσ):

4. Analysis of Frequency Distributions

Coefficient of Variation (C.V.):

Comprehensive Exam Strategy (Q&A)

Related Revision Notes

Conclusion

This post was curated by Jules, Exam Compass Bot, and edited for accuracy y Ayush.

📚 Related Topics

🚀 Ready to Ace Your Exam?

📚 Related Topics

🪤 The 5 Mistakes That Cost Marks

🔁 Last 5 Minutes Box

📋 Table of Contents

Statistics Class 11 Mathematics Revision — JEE 2026 Grandmaster Guide

What is Statistics Revision Notes?

Introduction

1. Measures of Dispersion

Key Measures:

2. Mean Deviation (M.D.)

Calculation Steps:

3. Variance and Standard Deviation

Variance (σ2\sigma^2σ2):

Standard Deviation (σ\sigmaσ):

4. Analysis of Frequency Distributions

Coefficient of Variation (C.V.):

Comprehensive Exam Strategy (Q&A)

Related Revision Notes

Conclusion

This post was curated by Jules, Exam Compass Bot, and edited for accuracy y Ayush.

📚 Related Topics

🚀 Ready to Ace Your Exam?

📚 Related Topics

🪤 The 5 Mistakes That Cost Marks

🔁 Last 5 Minutes Box

📋 Table of Contents

Statistics Class 11 Mathematics Revision — JEE 2026 Grandmaster Guide

What is Statistics Revision Notes?

Introduction

1. Measures of Dispersion

Key Measures:

2. Mean Deviation (M.D.)

Calculation Steps:

3. Variance and Standard Deviation

Variance (σ2\sigma^2σ2):

Standard Deviation (σ\sigmaσ):

4. Analysis of Frequency Distributions

Coefficient of Variation (C.V.):

Comprehensive Exam Strategy (Q&A)

Variance ( $\sigma^2$ ):

Standard Deviation ( $\sigma$ ):

Variance ( $\sigma^2$ ):

Standard Deviation ( $\sigma$ ):

Variance ( $\sigma^2$ ):

Standard Deviation ( $\sigma$ ):

Variance ( $\sigma^2$ ):

Standard Deviation ( $\sigma$ ):