NCERT Solutions Class 9 Maths Chapter 12 helps you understand Statistics through detailed solutions covering measures of central tendency—mean, median, and mode. You’ll learn how to calculate arithmetic mean using different methods, find median from ungrouped and grouped data, determine mode, and represent data using bar graphs and histograms. These fundamental statistical concepts are essential for data analysis in higher classes and real-world applications.
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Download PDF (Free)NCERT Solutions Class 9 Maths Chapter 12 Statistics – Complete Guide
NCERT Class 9 Chapter 12 – Statistics introduces you to the fascinating world of data analysis and interpretation. This chapter forms the foundation of statistical concepts that you’ll use throughout your academic journey and in real-life decision-making. With a weightage of 10 marks in the CBSE board exam and rated as easy difficulty, this is your opportunity to score full marks with proper practice and understanding.
📊 CBSE Class 9 Maths Chapter 12 – Exam Weightage & Marking Scheme
| CBSE Board Marks | 10 Marks |
| Unit Name | Statistics |
| Difficulty Level | Easy |
| Importance | Very High |
| Exam Types | CBSE Board, State Boards |
| Typical Questions | 2-3 questions |
You will explore how to systematically collect and organize raw data into meaningful forms like frequency distribution tables. The chapter covers three essential measures of central tendency – mean, median, and mode – which help you find the representative value of a dataset. You’ll learn multiple methods to calculate these measures, including the direct method, assumed mean method, and step deviation method for finding the mean. Understanding when to use which measure is crucial for solving real-world problems.
The graphical representation of data is another key component where you’ll work with bar graphs, histograms, and frequency polygons. These visual tools make data interpretation easier and are frequently asked in CBSE exams through both objective and descriptive questions. You’ll practice converting data between different graphical forms and extracting meaningful information from them.
Quick Facts – Class 9 Chapter 12
| 📖 Chapter Number | Chapter 12 |
| 📚 Chapter Name | Statistics |
| ✏️ Total Exercises | 1 Exercises |
| ❓ Total Questions | 9 Questions |
| 📅 Updated For | CBSE Session 2025-26 |
This chapter has very high importance for your board exams as questions from Statistics appear regularly in various formats – from 2-mark MCQs to 4-mark descriptive problems. The concepts you learn here connect directly to probability and advanced statistics in Class 10. Master this chapter with our comprehensive NCERT solutions, practice problems, and step-by-step explanations to build strong analytical skills that extend beyond mathematics into science, economics, and everyday life. With consistent practice, you can confidently secure all 10 marks from this chapter!
NCERT Solutions Class 9 Maths Chapter 12 – All Exercises PDF Download
Download exercise-wise NCERT Solutions PDFs for offline study
| Exercise No. | Topics Covered | Download PDF |
|---|---|---|
| EXERCISE 12.1 | Complete step-by-step solutions for 9 questions | 📥 Download PDF |
Statistics – Key Formulas & Concepts
Quick reference for CBSE exams
| Formula | Description | When to Use |
|---|---|---|
| Mean of Ungrouped Data \(\\bar{x} = \frac{\\sum x_i}{n}\\) | Calculates the average of a set of observations. Note: \(\\sum x_i\) means the sum of all observations, and \(n\) is the total number of observations. Make sure to add all values before dividing. | When you have raw data (ungrouped) and need to find the average value. |
| Mean of Grouped Data (Direct Method) \(\\bar{x} = \frac{\\sum f_i x_i}{\\sum f_i}\\) | Calculates the mean when data is grouped into classes with frequencies. Note: \(f_i\) is the frequency of each class, and \(x_i\) is the class mark (midpoint) of each class. Class mark is calculated as (Upper Limit + Lower Limit)/2 | When you have a frequency distribution table and need to find the mean. |
| Mean of Grouped Data (Assumed Mean Method) \(\\bar{x} = a + \frac{\\sum f_i d_i}{\\sum f_i}\\) | Calculates the mean using an assumed mean to simplify calculations. Note: \(a\) is the assumed mean (choose a value near the middle of the \(x_i\) values), and \(d_i = x_i – a\) is the deviation of each \(x_i\) from the assumed mean. This method reduces calculation errors. | When the values of \(x_i\) are large, making direct method calculations tedious. |
| Mean of Grouped Data (Step Deviation Method) \(\\bar{x} = a + h \cdot \frac{\\sum f_i u_i}{\\sum f_i}\\) | Calculates the mean using step deviation, further simplifying calculations. Note: \(u_i = \frac{x_i – a}{h}\), where \(h\) is the class size (assuming equal class sizes). This method is most efficient for large datasets with equal class intervals. | When the deviations \(d_i\) have a common factor \(h\). |
| Mode of Ungrouped Data Mode = Observation with highest frequency | The value that appears most frequently in a dataset. Note: Simply count how many times each value appears and choose the one that appears the most. A dataset can have more than one mode (bimodal, multimodal). | When you need to find the most common value in a set of observations. |
| Median of Ungrouped Data (Odd Number of Observations) Median = Value of the \(\\left(\\frac{n+1}{2}\\right)^{th}\) observation | The middle value when the data is arranged in ascending or descending order. Note: First, arrange the data in ascending order. \(n\) is the number of observations. | When you need to find the central tendency of the data and the data is not grouped. |
| Median of Ungrouped Data (Even Number of Observations) Median = \(\\frac{1}{2} \\left[ \\text{Value of } \\left(\\frac{n}{2}\\right)^{th} \\text{ observation } + \\text{ Value of } \\left(\\frac{n}{2} + 1\\right)^{th} \\text{ observation } \\right]\\) | The average of the two middle values when the data is arranged in ascending or descending order and the number of observations is even. Note: First, arrange the data in ascending order. \(n\) is the number of observations. Take the average of the two middle values. | When you need to find the central tendency of the data and the data is not grouped. |
| Cumulative Frequency Cumulative Frequency = Sum of frequencies up to that class | The running total of frequencies. Note: Add the frequency of each class to the cumulative frequency of the previous class. | Creating ogives (cumulative frequency curves) and finding the median of grouped data. |
| Class Mark \(\\text{Class Mark} = \\frac{\\text{Upper Class Limit + Lower Class Limit}}{2}\\) | The midpoint of a class interval. Note: Essential for finding \(x_i\) in grouped data calculations. | Calculating the mean of grouped data using any method (direct, assumed mean, or step deviation). |
Frequently Asked Questions – NCERT Class 9 Maths Chapter 12
📚 Related Study Materials – Class 9 Maths Resources
| Resource | Access |
|---|---|
| NCERT Class 9 Mathematics Textbook | Download Book |
| NCERT Class 9 Science Solutions | View Solutions |
| RD Sharma Class 9 (Updated 2025-26) | View Solutions |
| NCERT Class 9 English (Beehive) | Download Book |