NCERT Solutions Class 10 Maths Chapter 14 teaches you how to calculate mean, median, and mode for grouped data using direct, assumed mean, and step-deviation methods. You’ll learn to construct cumulative frequency tables, draw ogives, and find the median graphically—essential skills for analyzing real-world data in your board exams. Each solution includes detailed formulas, worked examples, and tips to avoid common calculation errors.
Download Complete Chapter 14 Solutions PDF
All exercises with step-by-step solutions | Updated 2025-26 | Free Download
Download PDF (Free)NCERT Solutions Class 10 Maths Chapter 14 Statistics – Complete Guide
NCERT Class 10 Chapter 14 Statistics takes you beyond basic data handling into the world of grouped data analysis, a crucial skill for CBSE board examinations. You’ll explore how to organize large datasets into class intervals and calculate the three measures of central tendency—mean (using direct, assumed mean, and step-deviation methods), median, and mode. This chapter builds directly on your Class 9 foundation and introduces you to more sophisticated statistical tools used in real-world research and data science.
📊 CBSE Class 10 Maths Chapter 14 – Exam Weightage & Marking Scheme
| CBSE Board Marks | 6 Marks |
| Unit Name | Statistics |
| Difficulty Level | Easy |
| Importance | High |
| Exam Types | CBSE Board, State Boards |
| Typical Questions | 2-3 questions |
The chapter holds significant importance in your CBSE Class 10 Mathematics exam, carrying 6 marks with relatively easy difficulty level. You’ll encounter questions asking you to find the mean of grouped data (3-4 marks), calculate median from cumulative frequency (2-3 marks), and determine mode using the modal class formula. The chapter also includes constructing and interpreting cumulative frequency curves (ogives), which are frequently tested in board examinations. Understanding the graphical method to find median gives you an alternative approach that examiners often appreciate.
Statistics isn’t just about calculations—it’s about making sense of information around you. Whether analyzing survey results, understanding economic data, or interpreting scientific research, these statistical tools are indispensable. You’ll learn to choose the most appropriate measure of central tendency based on data characteristics, a skill that demonstrates deeper mathematical thinking. The chapter also connects beautifully with probability concepts you’ll study later.
Quick Facts – Class 10 Chapter 14
| 📖 Chapter Number | Chapter 14 |
| 📚 Chapter Name | Statistics |
| ✏️ Total Exercises | 1 Exercises |
| ❓ Total Questions | 25 Questions |
| 📅 Updated For | CBSE Session 2025-26 |
With consistent practice of NCERT solutions and previous year CBSE questions, you’ll find Statistics to be a scoring chapter. Focus on understanding the formulas rather than memorizing them, practice diverse numerical problems, and pay special attention to the graphical methods. Mastering this chapter not only secures easy marks in your board exam but also equips you with analytical skills valuable for higher studies in science, commerce, and humanities streams.
NCERT Solutions Class 10 Maths Chapter 14 – All Exercises PDF Download
Download exercise-wise NCERT Solutions PDFs for offline study
| Exercise No. | Topics Covered | Download PDF |
|---|---|---|
| Exercise 14.1 | Complete step-by-step solutions for 25 questions | 📥 Download PDF |
Statistics – Key Formulas & Concepts
Quick reference for CBSE exams
| Formula | Description | When to Use |
|---|---|---|
| Mean (Direct Method) \(\\bar{x} = \\frac{\\sum f_i x_i}{\\sum f_i}\\) | Calculates the mean of a grouped data set 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 the class mark as (Upper Limit + Lower Limit)/2 | When the values of \(x_i\) and \(f_i\) are relatively small and easy to multiply. |
| Mean (Assumed Mean Method) \(\\bar{x} = a + \\frac{\\sum f_i d_i}{\\sum f_i}\\) | Calculates the mean of a grouped data set using the assumed mean method. Note: \(a\) is the assumed mean, and \(d_i = x_i – a\) is the deviation of \(x_i\) from the assumed mean. | When the values of \(x_i\) are large, making direct multiplication tedious. Choose a suitable ‘a’ (assumed mean) near the middle of the data. |
| Mean (Step Deviation Method) \(\\bar{x} = a + h \\frac{\\sum f_i u_i}{\\sum f_i}\\) | Calculates the mean of a grouped data set using the step deviation method. Note: \(a\) is the assumed mean, \(h\) is the class size, and \(u_i = \\frac{x_i – a}{h}\). Ensure that all class intervals are continuous before calculating. | When the class sizes are equal (h is constant) and the deviations are large multiples of h. This simplifies calculations significantly. |
| Mode (Grouped Data) \(Mode = l + \\frac{f_1 – f_0}{2f_1 – f_0 – f_2} \\times h\\) | Calculates the mode of a grouped data set. Note: \(l\) is the lower limit of the modal class, \(h\) is the class size, \(f_1\) is the frequency of the modal class, \(f_0\) is the frequency of the class preceding the modal class, and \(f_2\) is the frequency of the class succeeding the modal class. Don’t confuse \(f_0\) and \(f_2\). | When you need to find the most frequent value in a grouped data set. Identify the modal class first (class with highest frequency). |
| Median (Grouped Data) \(Median = l + \\frac{\\frac{n}{2} – cf}{f} \\times h\\) | Calculates the median of a grouped data set. Note: \(l\) is the lower limit of the median class, \(n\) is the total frequency (\(\\sum f_i\)), \(cf\) is the cumulative frequency of the class preceding the median class, \(f\) is the frequency of the median class, and \(h\) is the class size. Remember to calculate cf correctly. | When you need to find the middle value in a grouped data set. Find the median class first (class containing n/2). |
| Empirical Relationship (Mean, Median, Mode) \(3 Median = Mode + 2 Mean\\) | Relates the mean, median, and mode in a moderately skewed distribution. Note: This is an approximate relationship, and it may not be accurate for all distributions. Rearrange the formula to solve for the required variable. | When you are given two of the three values (mean, median, mode) and need to find the third. |
| Class Mark \(Class Mark = \\frac{Upper Limit + Lower Limit}{2}\\) | Calculates the midpoint of a class interval. Note: This is the average of the upper and lower limits of the class interval. | To find \(x_i\) in the direct method for calculating the mean. Also used in graphical representation. |
| Cumulative Frequency \(CF_i = CF_{i-1} + f_i\) | The cumulative frequency of a class is the sum of the frequencies of all classes up to and including that class. Note: Start with the first frequency as the first cumulative frequency, then keep adding the frequencies. | To determine the median class in a grouped data set. Essential for drawing Ogives. |
| Class Size \(h = Upper Limit – Lower Limit\) | Calculates the width of a class interval, assuming all class sizes are equal. Note: Ensure that the class intervals are continuous before calculating the class size. If intervals are discontinuous, adjust them by subtracting 0.5 from the lower limit and adding 0.5 to the upper limit. | In the assumed mean method and step deviation method for calculating the mean, and for calculating mode and median. |
Frequently Asked Questions – NCERT Class 10 Maths Chapter 14
📚 Related Study Materials – Class 10 Maths Resources
| Resource | Access |
|---|---|
| NCERT Class 10 Maths All Chapters | View Solutions |
| NCERT Class 10 Science Solutions | View Solutions |
| NCERT Class 10 Social Science | View Solutions |
| NCERT Class 10 English Solutions | View Solutions |