NCERT Solutions Class 11 Maths Chapter 13 teaches you how to analyze data using measures of dispersion like range, variance, and standard deviation. You’ll learn to calculate mean deviation about mean and median, find coefficient of variation to compare datasets, and understand how these statistical tools help interpret real-world data in economics, science, and research. Each solution shows the exact formula application and calculation steps needed for board exams.
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All exercises with step-by-step solutions | Updated 2025-26 | Free Download
Download PDF (Free)NCERT Solutions Class 11 Maths Chapter 13 Statistics – Complete Guide
NCERT Class 11 Chapter 13 Statistics builds upon your foundational knowledge from Class 10, introducing you to more sophisticated statistical tools that are essential for data analysis. You’ll explore measures of dispersion including range, quartile deviation, mean deviation, and standard deviation—concepts that help you understand how data spreads around the central value. This chapter also introduces you to variance and coefficient of variation, which are crucial for comparing different data sets.
📊 CBSE Class 11 Maths Chapter 13 – Exam Weightage & Marking Scheme
| CBSE Board Marks | 6 Marks |
| Unit Name | Statistics and Probability |
| Difficulty Level | Easy |
| Importance | High |
| Exam Types | CBSE Board, State Boards |
| Typical Questions | 2-3 questions |
This chapter carries significant weightage of 6 marks in CBSE board exams and is considered relatively easy, making it an excellent scoring opportunity. You’ll encounter various question types including 2-mark questions on basic concepts, 4-mark problems on calculating standard deviation and variance, and 6-mark questions involving analysis of frequency distributions. The chapter emphasizes both theoretical understanding and practical calculation skills, with special focus on shortcut methods for grouped data.
Statistics has immense practical applications in economics, business, science, and everyday decision-making. You’ll learn how companies analyze sales data, how scientists interpret experimental results, and how economists study market trends using these statistical measures. The concepts you master here form the foundation for probability distributions and inferential statistics in Class 12.
Quick Facts – Class 11 Chapter 13
| 📖 Chapter Number | Chapter 13 |
| 📚 Chapter Name | Statistics |
| ✏️ Total Exercises | 3 Exercises |
| ❓ Total Questions | 28 Questions |
| 📅 Updated For | CBSE Session 2025-26 |
With consistent practice of NCERT solutions and previous year CBSE questions, you can easily secure full marks from this chapter. Focus on understanding the formulas, practicing step-by-step calculations, and interpreting statistical results. Mastering Statistics not only boosts your board exam score but also develops analytical thinking skills valuable for competitive exams like JEE and for your future academic pursuits in any field involving data analysis.
NCERT Solutions Class 11 Maths Chapter 13 – All Exercises PDF Download
Download exercise-wise NCERT Solutions PDFs for offline study
| Exercise No. | Topics Covered | Download PDF |
|---|---|---|
| EXERCISE 13.1 | Complete step-by-step solutions for 12 questions | 📥 Download PDF |
| EXERCISE 13.2 | Complete step-by-step solutions for 10 questions | 📥 Download PDF |
| Miscellaneous Exercise on Chapter 13 | Complete step-by-step solutions for 6 questions | 📥 Download PDF |
Statistics – Key Formulas & Concepts
Quick reference for CBSE exams
| Formula | Description | When to Use |
|---|---|---|
| Mean (Ungrouped Data) \(\\bar{x} = \\frac{\\sum x_i}{n}\\) | Calculates the average of a set of ungrouped data values. Note: Make sure you add ALL the values and divide by the TOTAL number of values. | When you have a list of individual data points and need to find their average. |
| Mean (Grouped Data – Direct Method) \(\\bar{x} = \\frac{\\sum f_i x_i}{\\sum f_i}\\) | Calculates the average of grouped data using the direct method. Note: f_i is the frequency of the i-th class, and x_i is the class mark (midpoint) of the i-th class. Remember to find class mark: (Upper Limit + Lower Limit)/2 | When you have a frequency table (grouped data) and the numbers are relatively small. |
| Mean (Grouped Data – Assumed Mean Method) \(\\bar{x} = a + \\frac{\\sum f_i d_i}{\\sum f_i}\\) | Calculates the average of grouped data using the assumed mean method. Note: Choose an ‘a’ (assumed mean) close to the middle of the data range to simplify calculations. | When you have a frequency table (grouped data) and the numbers are large. ‘a’ is the assumed mean and d_i = x_i – a. |
| Mean (Grouped Data – Step Deviation Method) \(\\bar{x} = a + h \\frac{\\sum f_i u_i}{\\sum f_i}\\) | Calculates the average of grouped data using the step deviation method. Note: This method is most efficient when class intervals are equal and large. Remember to multiply by ‘h’! | When you have a frequency table (grouped data) and the class sizes are equal. u_i = (x_i – a)/h, h is the class size. |
| Variance (Ungrouped Data) \(\\sigma^2 = \\frac{1}{n} \\sum (x_i – \\bar{x})^2\\) | Measures the spread of data around the mean for ungrouped data. Note: First find the mean \\(\\bar{x}\\), then calculate the squared difference of each value from the mean. Divide by n (number of observations). | When you need to quantify the variability in a set of ungrouped data. |
| Variance (Grouped Data) \(\\sigma^2 = \\frac{1}{N} \\sum f_i (x_i – \\bar{x})^2\\) | Measures the spread of data around the mean for grouped data. Note: N = \\(\\sum f_i\\). Calculate the weighted squared difference of each class mark from the mean. | When you need to quantify the variability in a frequency distribution. |
| Standard Deviation (Ungrouped Data) \(\\sigma = \\sqrt{\\frac{1}{n} \\sum (x_i – \\bar{x})^2}\\) | Measures the spread of data around the mean; it is the square root of the variance. Note: It is the positive square root of the variance. Use it to compare the variability of different datasets. | When you want to understand the dispersion of data in the same units as the original data. |
| Standard Deviation (Grouped Data) \(\\sigma = \\sqrt{\\frac{1}{N} \\sum f_i (x_i – \\bar{x})^2}\\) | Measures the spread of grouped data around the mean; it is the square root of the variance. Note: Remember that N = \\(\\sum f_i\\). Take the square root of the grouped data variance. | When you want to understand the dispersion of grouped data in the same units as the original data. |
| Standard Deviation (Simplified Formula – Grouped Data) \(\\sigma = \\sqrt{\\frac{\\sum f_i x_i^2}{N} – (\\frac{\\sum f_i x_i}{N})^2}\\) | Alternative way to calculate standard deviation for grouped data, sometimes easier to compute. Note: N = \\(\\sum f_i\\). This formula avoids calculating (x_i – \\bar{x}) for each class. | When you want a more computationally efficient method for finding standard deviation of grouped data. |
| Coefficient of Variation \(CV = \\frac{\\sigma}{\\bar{x}} \\times 100\\) | Measures the relative variability of a dataset, independent of the units of measurement. Note: Expresses the standard deviation as a percentage of the mean. Higher CV means greater relative variability. | When you want to compare the variability of two or more datasets with different means or different units. |
Frequently Asked Questions – NCERT Class 11 Maths Chapter 13
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