NCERT Solutions for Class 10 Maths Chapter 13: Statistics
NCERT Solutions for Class 10 Maths Chapter 13 – Statistics – is a chapter that bridges mathematics with real-world data analysis. Every day, data is collected around us—from election results in Delhi to crop yields in Punjab, from temperature readings in Kerala to traffic surveys in Bengaluru. Chapter 13 teaches students how to make sense of this data using three powerful measures: Mean, Median, and Mode. For other chapters of NCERT Solutions for Class 10 Maths, check NCERT Solutions for Class 10 and NCERT Solutions.
These measures of central tendency are the backbone of the chapter and are heavily tested in CBSE board examinations. At Myclass24, we provide complete, step-by-step NCERT Solutions for Class 10 Maths Chapter 13 that cover all exercises and explain the logic behind each calculation method. Whether you are computing the mean of grouped data using the Step Deviation Method, finding the median from a frequency distribution table, or calculating the mode using the modal class formula, Myclass24 ensures that every solution is easy to follow and exam-ready. Students from all over India—whether from CBSE schools in urban cities or smaller towns—will find these solutions accessible and clearly explained. This chapter is especially important as it directly applies to everyday life, data interpretation, and analytical thinking skills required in higher studies.
Download PDF: NCERT Solutions for Class 10 Maths Chapter 13 – Statistics
Myclass24 offers a free downloadable PDF of NCERT Solutions for Class 10 Maths Chapter 13. The PDF covers Exercise 13.1 through Exercise 13.4 with full solutions, frequency distribution tables, and worked examples. The file is formatted for mobile screens so you can revise on your smartphone during travel or study breaks. All formulas are clearly stated before each solution so you can cross-reference and learn the method alongside the answer.
Chapter 13 – Concepts, Methods, and Exam Preparation
Chapter 13 of NCERT Class 10 Maths belongs to the Statistics and Probability unit. It deals with grouped data and introduces three measures of central tendency—Mean, Median, and Mode—along with their graphical representations through cumulative frequency curves (Ogives). Unlike earlier classes where statistics involved simple ungrouped data, this chapter requires working with class intervals, frequencies, and cumulative frequencies.
Methods for Calculating Mean
| Method | Formula | Best Used When |
| Direct Method | Σfx / Σf | Values are small |
| Assumed Mean Method | a + (Σfd / Σf) | Values are large |
| Step Deviation Method | a + h × (Σfu / Σf) | Class sizes are equal |
Summary of Measures of Central Tendency
| Measure | Definition | Formula / Method |
| Mean | Average of all values | Direct / Assumed / Step Deviation |
| Median | Middle value in ordered data | l + [(n/2 − cf)/f] × h |
| Mode | Most frequently occurring value | l + [(f1−f0)/(2f1−f0−f2)] × h |
Exercise-Wise Question Distribution
| Exercise | Topic | Questions |
| Ex 13.1 | Mean of Grouped Data | 9 Questions |
| Ex 13.2 | Mode of Grouped Data | 6 Questions |
| Ex 13.3 | Median of Grouped Data | 7 Questions |
| Ex 13.4 | Graphical Representation (Ogive) | 3 Questions |
Graphical Representation – Less Than and More Than Ogives
Exercise 13.4 deals with Ogives, which are cumulative frequency graphs. A less-than Ogive is drawn by plotting upper class boundaries against cumulative frequencies, while a more-than Ogive is plotted using lower class boundaries. The intersection point of both Ogives gives the Median of the data. This concept is visually intuitive and is often tested with a 4-mark question in CBSE board exams. Myclass24 solutions include step-by-step graph construction instructions along with table preparation to make this exercise easy.
Key Formula Facts
The Median formula used in this chapter is: l + [(n/2 − cf) / f] × h, where l = lower boundary of median class, n = total frequency, cf = cumulative frequency before median class, f = frequency of median class, and h = class size. The Mode formula is: l + [(f1 − f0) / (2f1 − f0 − f2)] × h, where f1 = frequency of modal class, f0 = frequency before modal class, and f2 = frequency after modal class. Myclass24 solutions clearly identify each variable with its value from the table to eliminate confusion.
FAQs on NCERT Solutions for Class 10 Maths Chapter 13: Statistics
The Statistics chapter focuses on collecting, organising, representing, and analysing numerical data. Students learn how to calculate measures of central tendency such as mean, median, and mode for grouped data. The chapter also introduces cumulative frequency and graphical representations that help interpret information effectively. Statistics is important because it helps summarise large amounts of data and draw meaningful conclusions. Understanding statistical methods improves analytical thinking and problem-solving skills. Since data analysis is widely used in education, business, science, and research, this chapter has significant practical value and examination importance.
The mean is the average value of a data set and is obtained by dividing the sum of all observations by the total number of observations. For grouped data, a systematic method is used to simplify calculations. The mean is important because it provides a single value that represents the overall trend of the data. It is commonly used in academic results, surveys, and statistical reports. Understanding how to calculate and interpret the mean helps students analyze information effectively and solve data-based questions with confidence.
The median is the middle value that divides a data set into two equal parts. For grouped data, students use cumulative frequency to determine the median class and then apply a formula to calculate the median. The median is particularly useful when data contains extreme values because it is not affected significantly by unusually high or low observations. Understanding the median helps students interpret data more accurately. Examination questions frequently involve calculating and analyzing median values from grouped frequency distributions.
The mode is the value or class that occurs most frequently in a data set. In grouped data, students identify the modal class and use a formula to determine the mode. The mode is useful because it shows the most common observation in a distribution. Businesses, researchers, and organizations often use mode to identify popular choices and trends. Understanding this concept helps students compare different measures of central tendency and interpret statistical information more effectively. Mode-based questions are commonly asked in board examinations.
Cumulative frequency is the running total of frequencies in a data table. It helps organize information and is essential for finding the median of grouped data. By arranging frequencies cumulatively, students can identify the position of observations within the data set more easily. Cumulative frequency tables simplify calculations and improve data interpretation. Understanding this concept is important because it connects statistical formulas with graphical and analytical methods. Examination questions often require students to construct cumulative frequency tables before calculating statistical measures.
Statistics is used in education, healthcare, economics, sports, business, and scientific research. It helps organizations collect data, analyze trends, and make informed decisions. Governments use statistical information to plan policies, while businesses rely on it to understand customer behavior. Sports analysts use statistics to evaluate player performance and team strategies. Learning Statistics helps students understand how numerical information is used in everyday life. It also develops analytical skills that are valuable across many academic and professional fields.
Students often make errors while calculating frequencies, cumulative frequencies, or class marks. Mistakes can also occur when selecting the median class or substituting values into formulas. Some students confuse mean, median, and mode, leading to incorrect interpretations. To avoid these errors, it is important to organize data carefully and verify calculations step by step. Regular practice with tables and statistical formulas improves accuracy. A clear understanding of concepts helps students perform well in examination questions related to data analysis.