CBSE Class 9 Mathematics Chapter 14: Statistics NCERT Solutions
This chapter on Statistics for CBSE Class 9 Mathematics introduces students to the fundamental concepts of data collection and representation. The exercises cover identifying examples of data, classifying data as primary or secondary, and constructing frequency distribution tables. Students will learn to organize raw data, count occurrences of different data points, and interpret these tables to find the most and least frequent occurrences. These solutions provide clear, step-by-step explanations to help students understand how to work with statistical data, making it an essential resource for exam preparation and building a strong foundation in statistics.
Quick info
| Board | CBSE |
|---|---|
| Class | Class 9 |
| Subject | Mathematics |
| Session | 2026 |
| Language | English |
| Type | NCERT Solutions |
| Chapter | Chapter 14: Statistics |
Chapter summary
Chapter 14, Statistics, for Class 9 Mathematics NCERT Solutions focuses on understanding and organizing data. It covers identifying real-world data examples, distinguishing between primary and secondary data, and creating frequency distribution tables to represent data. The solutions guide students through classifying and interpreting data sets, helping them identify common and rare occurrences within the data.
Learning outcomes
- Identify and provide examples of data collected in daily life.
- Differentiate between primary and secondary data.
- Classify given data as either primary or secondary.
- Construct frequency distribution tables for a given set of data.
- Interpret frequency distribution tables to find the most and least common data points.
Topics covered
Paper topics
- Data Collection
- Primary Data
- Secondary Data
- Classification of Data
- Frequency Distribution Table
- Interpretation of Data
- Most Common Data
- Rarest Data
Important topics
- Primary vs. Secondary Data
- Constructing Frequency Distribution Tables
- Interpreting Frequency Tables
- Identifying Most and Rarest Data Points
PDF preview
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Questions and Solutions
Question 1
We can collect various types of data from our daily lives. Here are five examples:
- The number of females per 1000 males in different states of our country.
- The weights of students in our classroom.
- The annual production of wheat in our country over the last ten years.
- The number of plants present in our local area or neighborhood.
- The amount of rainfall recorded in our city during the past ten years.
Question 2
Data can be classified as primary or secondary based on how it is collected:
- Primary Data: This is the information collected by the investigator directly for their specific purpose or objective. It is original data collected for the first time.
- Secondary Data: This is information that has already been collected by someone else and is available from various sources like published reports, books, or websites. The investigator uses this pre-existing data.
Applying these definitions to the examples in Question 1:
- 1. Number of females per 1000 males in various states: This data is usually available from government census reports or statistical organizations, making it secondary data.
- 2. Weights of students of our class: This data is collected directly by measuring each student, so it is primary data.
- 3. Production of wheat in the last 10 years: This information is typically obtained from agricultural reports or government statistics, making it secondary data.
- 4. Number of plants in our locality: If we count the plants ourselves, it's primary data.
- 5. Rainfall in our city in the last 10 years: This data is usually available from meteorological departments or weather reports, making it secondary data.
Therefore, the data in examples 2 and 4 are primary, while the data in examples 1, 3, and 5 are secondary.
Question 1
To represent the data in a frequency distribution table, we need to count the occurrences of each blood group among the 30 students.
Let's tally the blood groups:
- A: Count the number of 'A's. There are 9 'A's.
- B: Count the number of 'B's. There are 6 'B's.
- AB: Count the number of 'AB's. There are 3 'AB's.
- O: Count the number of 'O's. There are 12 'O's.
The total number of students is 9 + 6 + 3 + 12 = 30, which matches the given total.
Now, we can construct the frequency distribution table:
| Blood Group | Number of Students (Frequency) |
|---|---|
| A | 9 |
| B | 6 |
| AB | 3 |
| O | 12 |
| Total | 30 |
To determine the most common and rarest blood groups, we look at the frequencies:
- The highest frequency is 12, which corresponds to blood group O. So, O is the most common blood group.
- The lowest frequency is 3, which corresponds to blood group AB. So, AB is the rarest blood group.
Answer: The most common blood group among these students is O, and the rarest blood group is AB.
Common mistakes
- Confusing primary and secondary data definitions.
- Errors in counting data points for frequency tables.
- Misinterpreting the most and least common data from a table.
Revision tips
- Practice identifying real-world data examples and classifying them.
- Focus on accurately tallying data points to build correct frequency tables.
- Review the definitions of primary and secondary data to avoid confusion.
- Pay close attention to interpreting the frequency table to answer questions about common and rare data.
Practice MCQs
Q1. Which of the following is an example of data collected from day-to-day life?
Explanation: Production of wheat in the last 10 years is a type of data that can be collected and observed in daily life, unlike astronomical or fundamental scientific constants.
Q2. Data collected by the investigator for their own purpose is called:
Explanation: Primary data is defined as the information collected firsthand by the researcher for a specific objective.
Q3. When information is gathered from a source that has already collected it, it is known as:
Explanation: Secondary data is information that has already been collected and processed by someone else and is being used by a new investigator.
Q4. In a frequency distribution table, the 'frequency' represents:
Explanation: The frequency in a distribution table indicates how many times a specific data value or category occurs in the dataset.
Q5. If 12 students have blood group O and 3 students have blood group AB, which is the most common and rarest blood group respectively among these students?
Explanation: The most common blood group is the one with the highest frequency (O with 12 students), and the rarest is the one with the lowest frequency (AB with 3 students).
Frequently asked questions
What is the main focus of Chapter 14: Statistics for Class 9 Maths?
Chapter 14 focuses on understanding and organizing data, including collecting examples, classifying data as primary or secondary, and creating frequency distribution tables.
What is the difference between primary and secondary data?
Primary data is collected by the investigator for their own purpose, while secondary data is obtained from a source that has already collected and stored the information.
How do I create a frequency distribution table?
To create a frequency distribution table, you list each distinct data value or category and then count how many times each value appears in the dataset, recording this count as the frequency.
How can these NCERT Solutions help with exam revision?
These solutions provide clear, step-by-step explanations for each question, helping students understand the concepts and methods used in statistics, which is crucial for revising the chapter effectively for exams.
What does it mean to find the 'most common' or 'rarest' blood group in a data set?
The 'most common' data point is the one with the highest frequency (appears most often), and the 'rarest' data point is the one with the lowest frequency (appears least often) in the given dataset.
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