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NCERT Solutions for Class 9 Maths Chapter 12 Statistics

• NCERT Solutions
• Chapter 14 Statistics

NCERT Solutions for Maths Class 9 Chapter 12 Statistics - FREE PDF Download

NCERT Solutions for Maths Class 9 Chapter 12 Statistics is one of the most important chapters that carries good marks, so learning this chapter correctly using Chapter 12 Statistics Class 9 NCERT Solutions is necessary. Class 9 Maths Chapter 14 Statistics is thus highly important from the examination’s perspective. The chapter covers data from the statistical aspect, grouping data, presenting data in a specific manner, the idea of primary and secondary data, and developing grouped frequency distribution tables.

Get ready to unlock patterns, compare data sets, and better understand the world around you! Class 9 Maths Ch 12 PDF Solutions is provided below. The NCERT solutions provide step-by-step explanations, making it easier to grasp complex topics. By practising Class 9 Maths Ch 12 PDF, students can confidently strengthen their analytical skills and prepare for exams.

Glance on Class 9 Maths Chapter 12 - Statistics

Understanding the concept of data and its different types (numerical, categorical).

Exploring methods for collecting data like surveys, experiments, and observations.

Mastering how to represent data visually using Data Representation:

Bar Graphs: Illustrating comparisons between categories.

Histograms: Depicting the frequency distribution of numerical data.

Organizing data into categories and calculating their frequencies (how often each category appears).

Measures of Central Tendency: 

Mean (average): The sum of all values divided by the number of values.

Median: The middle value when data is arranged in ascending or descending order.

Mode: The most frequent value in the data set.

This article contains chapter notes, important questions, exemplar solutions, exercises and video links for Chapter 12 - Statistics, which you can download as PDFs.

There is only one exercise in Class 9th Maths Chapter 12 Statistics and 9 fully solved questions.

Access Exercise wise NCERT Solutions for Class 9 Maths Chapter 12

Exercises Under NCERT Solutions for Class 9 Maths Chapter 12 Statistics

Ncert solutions for class 9 maths chapter 12, "statistics," deals with the concepts related to the collection, organization, analysis, interpretation, and presentation of data. the chapter consists of the following exercises: exercise 12.1: exercise 12.1 covers the graphical representation of data using histograms and frequency polygons. students learn to construct histograms by dividing data into intervals and plotting frequencies as bars, which visually display data distribution. frequency polygons involve plotting midpoints of intervals and connecting them with lines, aiding in data comparison and trend analysis. this exercise enhances students' skills in data visualization and interpretation., access ncert solutions for class 9 maths chapter 12 – statistics, exercise  12.1.

1. A survey conducted by an organisation for the cause of illness and death among the women between the ages \[15 - 44\] (in years) worldwide, found the following figures (in %)

i. Represent the information given above graphically.

Ans: The graph of the information presented above can be produced as follows by depicting causes on the x-axis and family fatality rate on the y-axis, and selecting an acceptable scale (1 unit = 5% for the y axis).

All the rectangle bars are of the same width and have equal spacing between them.

ii. Which condition is the major cause of women’s ill health and death worldwide?

Ans: Reproductive health issues are the leading cause of women's illness and mortality globally, affecting 31.8% of women.

iii. Try to find out, with the help of your teacher, any two factors which play a major role in the cause in (ii) above being the major cause

Ans: The factors are as follows:

a. Lack of medical facilities

b. Lack of correct knowledge of treatment

2. The following data on the number of girls (to the nearest ten) per thousand boys in different sections of Indian society is given below:

i. Represent the information above by a bar graph.

Ans: The graph of the information presented above may be built by choosing an appropriate scale (1 unit = 100 girls for the y-axis) and representing section (variable) on the x-axis and number of girls per thousand boys on the y-axis.

Here, all the rectangle bars are of the same length and have equal spacing in between them.

ii. In the classroom discuss what conclusions can be arrived at from the graph.

Ans: The largest number of females per thousand boys (i.e., 970) is found in ST, while the lowest number of girls per thousand boys (i.e., 910) is found in urban areas.

In addition, the number of females per thousand boys is higher in rural regions than in cities, in backward districts than in non-backward districts, and in SC and ST districts than in non-SC/ST districts.

3. Given below are the seats won by different political parties in the polling outcome of a state assembly elections:

i. Draw a bar graph to represent the polling results.

ii. Which political party won the maximum number of seats?

Ans: From the above graph it is clear that Political party ‘A’ won the maximum number of seats.

4. The length of\[40\] leaves of a plant are measured correct to one millimeter, and the obtained data is represented in the following table:

i. Draw a histogram to represent the given data.

Ans: The length of leaves is represented in a discontinuous class interval with a difference of \[1\] between them, as can be seen. To make the class intervals continuous, \[\dfrac{1}{2} = 0.5\] must be added to each upper class limit and \[0.5\] must be subtracted from the lower class limits.

The above histogram may be built using the length of leaves on the x-axis and the number of leaves on the y-axis.

On the y-axis, one unit symbolises two leaves.

ii. Is there any other suitable graphical representation for the same data?

Ans: Frequency polygon is another good graphical representation of this data.

iii. Is it correct to conclude that the maximum number of leaves are 153 mm long? Why?

Ans: No, because the maximum number of leaves (i.e.\[12\]) has a length of \[144.5{\text{mm}}\] to \[153.5{\text{mm}}\] It is not necessary for all of them to be \[153{\text{mm}}\]long.

5. The following table gives the life times of neon lamps: 

\[\boxed{\begin{array}{*{20}{c}}  {{\text{ Length (in hours) }}}&{{\text{ Number of lamps}}} \\   {300 - 400}&{14} \\   {400 - 500}&{56} \\   {500 - 600}&{60} \\   {600 - 700}&{86} \\   {700 - 800}&{74} \\   {800 - 900}&{62} \\   {900 - 1000}&{48} \\   {}&{} \end{array}}\]

i. Represent the given information with the help of a histogram.

Ans: The histogram of the given data may be produced by plotting the life duration (in hours) of neon lamps on the x-axis and the number of lamps on the y-axis. Here,1

Here, 1 unit on the y-axis represents 10 lamps.

ii. How many lamps have a lifetime of more than \[700\] hours?

Ans: It may be deduced that the number of neon lamps with a lifetime more than \[700\]is equal to the sum of the numbers of neon lamps with lifetimes of \[700,800\]and \[900\]. As a result, there are \[184\] neon bulbs with a lifetime of more than \[700\] hours \[(74 + 62 + 48 = 184)\].

6. The following table gives the distribution of students of two sections according to the mark obtained by them:

Represent the marks of the students of both the sections on the same graph by two frequency polygons. From the two polygons compare the performance of the two sections.

Ans: We can find the class marks of the given class intervals by using the following formula.

\[{\text{Class mark  = }}\dfrac{{{\text{Upper class limit  +  Lower class limit}}}}{2}\]

The frequency polygon can be constructed as follows, with class markings on the x-axis and frequency on the y-axis, and an appropriate scale \[(1{\text{ unit  =  3 for the y - axis}})\].

It can be observed that the performance of students of section ‘A’ is better than the students of section ‘B’ in terms of good marks.

7. The runs scored by two teams A and B on the first 60 balls in a cricket match are given below:

\[\boxed{\begin{array}{*{20}{c}} {{\text{ }}\underline {{\text{Number of balls}}} {\text{ }}}&{{\text{ }}\underline {{\text{Class mark}}} {\text{ }}}&{{\text{ }}\underline {{\text{Team A}}} {\text{ }}}&{{\text{ }}\underline {{\text{Team B}}} {\text{ }}} \\   {0.5 - 6.5}&{3.5}&2&5 \\   {6.5 - 12.5}&{9.5}&1&6 \\   {12.5 - 18.5}&{15.5}&8&2 \\   {18.5 - 24.5}&{21.5}&9&{10} \\   {24.5 - 30.5}&{27.5}&4&5 \\  {30.5 - 36.5}&{33.5}&5&6 \\   {36.5 - 42.5}&{39.5}&6&3 \\  {42.5 - 48.5}&{45.5}&{10}&4 \\   {48.5 - 54.5}&{51.5}&6&8 \\  {54.5 - 60.5}&{57.5}&2&{10} \\   {}&{}&{}&{} \end{array}}\]

Represent the data of both the teams on the same graph by frequency polygons. 

(Hint: First make the class intervals continuous.)

Ans: A frequency polygon can be created by plotting class grades on the x-axis and running times on the y-axis.

8. A random survey of the number of children of various age groups playing in park was found as follows:

\[\boxed{\begin{array}{*{0}{c}}  {\underline {{\text{Age (in years)}}} }&{\underline {{\text{Number of children }}} }      \\   {{\text{1 - 2}}}&{\text{5}} \\   {{\text{2 - 3}}}&{\text{3}} \\   {{\text{3 - 5}}}&{\text{6}} \\ {{\text{5 - 7}}}&{{\text{12}}} \\  {{\text{7 - 10}}}&{\text{9}} \\   {{\text{10 - 15}}}&{{\text{10}}} \\   {{\text{15 - 17}}}&{\text{4}}    \end{array}}\]

Draw a histogram to represent the data above.

9. \[100\] surnames were randomly picked up from a local telephone directory and a frequency distribution of the number of letters in the English alphabet in the surnames was found as follows:

i. Draw a histogram to depict the given information.

The histogram can be generated using the number of letters on the x-axis and the fraction of the number of surnames per 2 letters interval on the y-axis, as well as an acceptable scale (1 unit = 4 students for the y axis).

ii. Write the class interval in which the maximum number of surnames lie.

Ans: The maximum number of surnames in the class interval is 6-8 since it contains 44 surnames, which is the maximum for this data.

Overview of Deleted Syllabus for CBSE Class 9 Maths Statistics

Class 9 Maths Chapter 12: Exercises Breakdown

Maths NCERT Class 9 Statistics Chapter has equipped you with valuable tools to transform raw data into meaningful insights. You've explored various methods for data collection and delved into the power of visual representations like bar graphs and histograms. By organizing data into frequency distributions, you've learned to summarize large datasets effectively. Furthermore, you've grasped the significance of central tendency measures (mean, median, mode) in understanding the "typical" value within a data set. In previous years exams, around 2-3 questions have been asked from Class 9 Maths Ch Statistics.

Other Study Material for CBSE Class 9 Maths Chapter 12

Chapter-Specific NCERT Solutions for Class 9 Maths

Given below are the chapter-wise NCERT Solutions for Class 9 Maths. Go through these chapter-wise solutions to be thoroughly familiar with the concepts.

FAQs on NCERT Solutions for Class 9 Maths Chapter 12 Statistics

1. How can we find the median of grouped data?

From the class intervals and the corresponding frequency, write the cumulative frequency(cf) in the third column. On finding n/2, locate the median class whose cumulative frequency is greater than and nearest to n/2.

Now Median = l +  (((n/2) - cf) / f) h

Where l = lower limit of the median class

n = no. of observations

cf = cumulative frequency of the class preceding the median class

f = frequency of the median class

h = class size ( where class sizes are equal)

2. What is the relationship between mean, median and mode of a data set?

In the case of any data set, the mean, median and mode are related by the following equation:

Mode = 3 Median - 2 Mean

Any problem on central tendency, that is mean, median and mode can be solved using this formula or a spin-off from the same.

3. Give five examples of data that you can collect from your day-to-day life.

Five examples from day-to-day life:

Number of students in our class

Number of fans in our school

Electricity bills for our house for the last two years

Election results obtained from television or newspapers

Literacy rate figures obtained from the Educational Survey

4. What are the three measures of central tendency for ungrouped data?

The three measures of central tendency are Mean, Median and mode.

5. When are frequency polygons used?

Frequency polygons are used when data is very large and continuous.  It is generally used to compare two different sets of data of the same nature. For example, comparing the performance of two different sections of the same class.

6. What is the main focus of 12th Ch Statistics Class 9?

The 12th Ch Statistics Class 9 is centered on cumulative frequency distributions. It teaches students how to construct cumulative frequency tables and graphs, which help in understanding data trends and distributions more comprehensively.

7. How do cumulative frequency graphs help in data analysis in Chapter 12 statistics class 9?

Cumulative frequency graphs, or ogives, assist in visualizing the running total of frequencies. They are useful for determining the median, quartiles, and percentiles, making it easier to analyze the spread and concentration of data points.

8. What are the key skills students develop in class 9th statistics?

In class 9th statistics , students develop skills in creating cumulative frequency tables, drawing ogives, and interpreting these graphs. These skills are essential for summarizing large data sets and making informed statistical inferences.

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Chapter 12 Class 9 Statistics

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Updated for 2023-24 NCERT Book.

Get solutions of all NCERT Questions of Chapter 12 Class 9 Statistics. All exercise questions and examples are solved with detailed explanations of each and every question.

In this chapter, we will learn

• The difference between primary and secondary data
• Representing raw data as ungrouped and grouped frequency distribution table
• Representing data as a bar graph
• Drawing a histogram - with uneven class interval
• Drawing frequency polygon - with and without a histogram
• Finding mean , median and mode of raw data

Click on a NCERT Exercise below, or start the chapter from the concepts given below.

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Assignments For Class 9 Mathematics Statistics

Assignments for Class 9 Mathematics Statistics have been developed for Standard 9 students based on the latest syllabus and textbooks applicable in CBSE, NCERT and KVS schools. Parents and students can download the full collection of class assignments for class 9 Mathematics Statistics from our website as we have provided all topic wise assignments free in PDF format which can be downloaded easily. Students are recommended to do these assignments daily by taking printouts and going through the questions and answers for Grade 9 Mathematics Statistics. You should try to do these test assignments on a daily basis so that you are able to understand the concepts and details of each chapter in your Mathematics Statistics book and get good marks in class 9 exams.

Key Concepts for Class 9 Mathematics Statistics

• There are two types of data (i) Primary (ii) Secondary • We can represent the data by (i) ungrouped and grouped frequency distribution. • Data can also represent by (i) bar graph (ii) Histogram (iii) Frequency polygons * Class mark of grouped data is lower limit + upper limit /2 * Measure of central tendencies by mean, median, mode. * Mean (x) = sum of all observations/total no. of observations If observations denoted by and their occurrence i.e. frequency is denoted by then mean is (x̅) = Σfixi/Σfi * Median: Arrange the observations in ascending or descending order then if numbers of observations (n) are odd then then median is (n+1/2)th term. If no. of observations (n) are even then median is average of and th terms. * Mode: The observation whose frequency is greatest. * Mode = 3 median – 2 mean.

Class 9 Mathematics Statistics Assignments

Class 9 Mathematics Statistics Important Questions and Answers

Question. Tally marks are used to find ………….

Question. Find the median of 37, 31, 42, 43, 46, 25, 39, 45, 32

Question. The following marks were obtained by the students in a test. 81, 72, 90, 90, 86, 85, 92, 70, 71, 83, 89, 95, 85, 79, 62 What is the range?

Question. If x, x 2 ……….x n are n values of a variable X such that

n=30, mean = 17/3

Question. In a histogram, each class rectangle is constructed with base as (a) frequency (b) class interval (c) range (d) size of the class

Question. If the mean of 2, 4, 6, 8, x, y is 5 then find the value of x+y.

Question. The mean of 10 numbers is 20, If 5 is subtracted from every number, what will be the new mean.

Question. Find the mode of following series. 25, 23, 22, 22, 24, 27, 27, 25, 23, 22, 26, 32

Question. Write the class mark of 90-110 group.

Question. Find the mean of first 10 even natural no.

Question. If the median of a series of data is 3 and mean is 2 then find the mode.

Question. If the mean of the following distribution is 6, then find the value of p.          x    2    4    6    10    p+5          f    3    2    3      1    2

Question. If the ratio of mean and median of a certain data is 2:3, then find the ratio of its mode and mean.

Question. Calculate the mean for the following distribution.       x   5   6    7     8   9       f   4   8   14   11   3

Question. Find the value of p, if the mean of following distribution is 20.

Question. The mean of 5 numbers is 18. If one number is excluded, their mean is 16, find the excluded number.

Question. The following observations have been arranged in ascending order. If the median of the data is 63, find the value of x. 29, 32, 48, 50, x, x+2, 72, 78, 84, 95

Question. Find the median of the following data 19, 25, 59, 48, 35, 31, 30, 32, 51. If 25 is replaced by 52, what will be the new median.

Question. Find the value of x and y in following distribution if it known that the mean of the distribution is 1.46.

Question. If the mean of five observations x, x+2, x+4, x+6, x+8 is 11 find the mean of first three observation.

Question. Given below is a cumulative frequency distribution table showing the age of people living in a locality. Age in years      No. of persons Above 108                 0 Above 96                   1 Above 84                   3 Above 72                   5 Above 60                   20 Above 48                   158 Above 36                   427 Above 24                   809 Above 12                   1026 Above 0                     1124 Prepare a frequency distribution table.

Question. The marks scored by 55 students in a test are given below :

Question. The mean monthly salary of 10 members of a group is Rs. 1445, one more member whose monthly salary is Rs. 1500 has joined the group. Find the mean monthly salary of 11 members of the group.

Question. The mean of 200 items was 50. Later on, it was discovered that the two items were misread as 92 and 8 instead of 192 and 88. Find the correct mean.

Assignments for Class 9 Mathematics Statistics as per CBSE NCERT pattern

All students studying in Grade 9 Mathematics Statistics should download the assignments provided here and use them for their daily routine practice. This will help them to get better grades in Mathematics Statistics exam for standard 9. We have made sure that all topics given in your textbook for Mathematics Statistics which is suggested in Class 9 have been covered ad we have made assignments and test papers for all topics which your teacher has been teaching in your class. All chapter wise assignments have been made by our teachers after full research of each important topic in the textbooks so that you have enough questions and their solutions to help them practice so that they are able to get full practice and understanding of all important topics. Our teachers at https://www.assignmentsbag.com have made sure that all test papers have been designed as per CBSE, NCERT and KVS syllabus and examination pattern. These question banks have been recommended in various schools and have supported many students to practice and further enhance their scores in school and have also assisted them to appear in other school level tests and examinations. Its easy to take print of thee assignments as all are available in PDF format.

Some advantages of Free Assignments for Class 9 Mathematics Statistics

• Solving Assignments for Mathematics Statistics Class 9 helps to further enhance understanding of the topics given in your text book which will help you to get better marks
• By solving one assignment given in your class by Mathematics Statistics teacher for class 9 will help you to keep in touch with the topic thus reducing dependence on last minute studies
• You will be able to understand the type of questions which are expected in your Mathematics Statistics class test
• You will be able to revise all topics given in the ebook for Class 9 Mathematics Statistics as all questions have been provided in the question banks
• NCERT Class 9 Mathematics Statistics Workbooks will surely help you to make your concepts stronger and better than anyone else in your class.
• Parents will be able to take print out of the assignments and give to their child easily.

All free Printable practice assignments are in PDF single lick download format and have been prepared by Class 9 Mathematics Statistics teachers after full study of all topics which have been given in each chapter so that the students are able to take complete benefit from the worksheets. The Chapter wise question bank and revision assignments can be accessed free and anywhere. Go ahead and click on the links above to download free CBSE Class 9 Mathematics Statistics Assignments PDF.

You can download free assignments for class 9 Mathematics Statistics from https://www.assignmentsbag.com

You can get free PDF downloadable assignments for Grade 9 Mathematics Statistics from our website which has been developed by teachers after doing extensive research in each topic.

On our website we have provided assignments for all subjects in Grade 9, all topic wise test sheets have been provided in a logical manner so that you can scroll through the topics and download the worksheet that you want.

You can easily get question banks, topic wise notes and questions and other useful study material from https://www.assignmentsbag.com without any charge

Yes all test papers for Mathematics Statistics Class 9 are available for free, no charge has been put so that the students can benefit from it. And offcourse all is available for download in PDF format and with a single click you can download all assignments.

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NCERT Solutions for Class 9 Maths Chapter 14 Statistics

Ncert solutions for class 9 maths chapter 14 statistics| pdf download.

• Exercise 14.1 Chapter 14 Class 9 Maths NCERT Solutions
• Exercise 14.2 Chapter 14 Class 9 Maths NCERT Solutions
• Exercise 14.3 Chapter 14 Class 9 Maths NCERT Solutions
• Exercise 14.4 Chapter 14 Class 9 Maths NCERT Solutions

NCERT Solutions for Class 9 Maths Chapters:

What are the benefits of NCERT Solutions for Chapter 14 Statistics Class 9 NCERT Solutions?

Find the range of the data 9, 7, 5, 7, 9, 9, 6, 18, 9 and 8., what do you mean by grouped data, what is the class-mark of the class 130 – 150, contact form.

NCERT Solutions for Class 6, 7, 8, 9, 10, 11 and 12

Important Questions for CBSE Class 9 Mathematics Statistics

October 11, 2018 by Bhagya

Important Questions for CBSE  Class 9 Mathematics Chapter 7 Statistics

The topics and sub-topics in NCERT Class 9 Maths Text Book Chapter 14 Statistics:

• Introduction
• Collection Of Data
• Presentation Of Data
• Graphical Representation Of Data
• Measures Of Central Tendency

IMPORTANT QUESTIONS

VERY SHORT ANSWER TYPE QUESTIONS 1. Mean of 20 observations is 17. If in the observations, observation 40 is replaced by 12, find the new mean. [CBSE-14-ERFKZ8H] Answer. Since mean of 20 observations is 17 Sum of the 20 observations = 17 x 20 = 340 New sum of 20 observations = 340 – 40 + 12 = 312 Newmean=312 / 20 =15.6

More Resources for CBSE Class 9

NCERT Solutions

• NCERT Solutions Class 9 Maths
• NCERT Solutions Class 9 Science
• NCERT Solutions Class 9 Social Science
• NCERT Solutions Class 9 English
• NCERT Solutions Class 9 Hindi
• NCERT Solutions Class 9 Sanskrit
• NCERT Solutions Class 9 IT
• RD Sharma Class 9 Solutions

3. Mean of 36 observations is 12. One observation 47 was misread as 74. Find the correct mean. [CBSE-14-17DIG1U] Answer. Mean of 36 observations = 12 Total of 36 observations = 36 x 12 = 432 Correct sum of 36 observations = 432 – 74 + 47 = 405 Correct mean of 36 observations =  405/ 36 =11.25

7. Write the class mark of an interval 90 – 120. Answer.  Classmark= (90+120 )/ 2  = 210 / 2 =105

9. Find the range of the given data : 25, 18, 20, 22, 16, 6, 17, 15, 12, 30, 32, 10, 19, 8, 11, 20 Answer. Here, the minimum and maximum values of given data are 6 and 32 respectively. Range = 32 – 6 = 26

13. Find the mode of the following scores : 14, 25, 14, 28, 18, 17, 18, 14, 23, 22, 14, 18 Answer. 14 repeat maximum number of times (4 times) in the given data. Mode = 14

• Write the lower limit of first class interval.
• Determine the class limits of the fourth class interval.
• Find the class mark of the class 45 – 50.
• Determine the class size. [CBSE March 2012]
• First class interval is 15 – 20 and its lower limit is 15.
• Fourth class interval is 30 – 35 Lower limit is 30 and upper limit is 35.
• Class  mark  of the class 45 – 50 =( 45+50 )/ 2  =95 / 2  =47.5
•  Class size = Upper limit of each class interval – Lower limit of each class interval .•. Here, class size = 20 – 15 = 5

NCERT Solutions for Class 9 Maths

• Chapter 1 Number systems
• Chapter 2 Polynomials
• Chapter 3 Coordinate Geometry
• Chapter 4 Linear Equations in Two Variables
• Chapter 5 Introduction to Euclid Geometry
• Chapter 6 Lines and Angles
• Chapter 7 Triangles
• Chapter 8 Quadrilaterals
• Chapter 9 Areas of Parallelograms and Triangles
• Chapter 10 Circles
• Chapter 11 Constructions
• Chapter 12 Heron’s Formula
• Chapter 13 Surface Areas and Volumes
• Chapter 14 Statistics
• Chapter 15 Probability
• Class 9 Maths (Download PDF)

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NCERT Exemplar for Class 9 Maths Chapter 14

Ncert exemplar for class 9 maths chapter 14 – statistics and probability.

Download the NCERT Exemplar Problem Solutions for Class 9 Maths Chapter 14 – Statistics and Probability solved by Mathematics Expert Teachers at Mathongo.com as per CBSE (NCERT) Book guidelines. By Preparing Exercise wise Exemplar Questions with Solutions to help you to revise complete Syllabus and Score More marks in your exams.

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Class 9 Mathematics Statistics Worksheets

We have provided below free printable  Class 9 Mathematics Statistics Worksheets  for Download in PDF. The worksheets have been designed based on the latest  NCERT Book for Class 9 Mathematics Statistics . These  Worksheets for Grade 9 Mathematics Statistics  cover all important topics which can come in your standard 9 tests and examinations. Free printable worksheets for CBSE Class 9 Mathematics Statistics , school and class assignments, and practice test papers have been designed by our highly experienced class 9 faculty. You can free download CBSE  printable worksheets for Mathematics Statistics Class 9 with solutions and answers. All worksheets and test sheets have been prepared by expert teachers as per the latest Syllabus in Mathematics Statistics Class 9. Students can click on the links below and download all Pdf  worksheets for Mathematics Statistics class 9  for free. All latest Kendriya Vidyalaya Class 9 Mathematics Statistics Worksheets  with Answers and test papers are given below.

Mathematics Statistics Class 9 Worksheets Pdf Download

Here we have the biggest database of free  CBSE NCERT KVS  Worksheets for Class 9  Mathematics Statistics . You can download all free Mathematics Statistics worksheets in Pdf for standard 9th. Our teachers have covered Class 9 important questions and answers  for Mathematics Statistics as per the latest curriculum for the current academic year. All test sheets question banks for Class 9 Mathematics Statistics and  CBSE Worksheets for Mathematics Statistics Class 9 will be really useful for Class 9 students to properly prepare for the upcoming tests and examinations. Class 9th students are advised to free download in Pdf all printable workbooks given below.

Topicwise Worksheets for Class 9 Mathematics Statistics Download in Pdf

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• As we have the best collection of Mathematics Statistics worksheets for Grade 9, you will be able to find important questions which will come in your class tests and examinations.
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Tim Walz, Who Spent Decades as an Enlisted Soldier, Brings Years of Work on Vets Issues to Dem Ticket

A retired Army National Guard noncommissioned officer who was once the top Democrat on the House Veterans Affairs Committee could become the next vice president.

Presumptive Democratic presidential nominee Vice President Kamala Harris announced Tuesday that Minnesota Gov. Tim Walz will be her running mate. That puts someone with an enlisted background on both presidential tickets after Republican nominee former President Donald Trump chose Marine veteran Sen. JD Vance of Ohio as his running mate.

Patrick Murphy, an Army veteran who was Walz' roommate when they were both freshmen in Congress, called Walz a "soldier's soldier."

Read Next: A Rocket Attack at an Iraqi Military Base Injures US Personnel, Officials Say

"The two largest federal agencies are DoD and the VA, so someone who has intimate knowledge of both is incredibly important," Murphy, who served as Army under secretary during the Obama administration, said in a phone interview with Military.com. "He was a field artilleryman who has tinnitus as diagnosed by the VA, so he understands the plight of our brother and sister veterans."

Walz enlisted in the Army National Guard in Nebraska in 1981 and retired honorably in 2005 as the top enlisted soldier for 1st Battalion, 125th Field Artillery Regiment, in the Minnesota National Guard, according to a copy of his records provided by the Minnesota Guard. He reached the rank of command sergeant major and served in that role, but he officially retired as a master sergeant for benefits purposes because he didn't finish a required training course, according to the records and a statement from the Minnesota Guard.

His Guard career included responding to natural disasters in the United States, as well as a deployment to Italy to support U.S. operations in Afghanistan, according to a 2018 article by Minnesota Public Radio . Walz earned several awards, including the Army Commendation Medal and two Army Achievement Medals, according to his military records. Working a civilian job as a high school teacher and football coach, the Nebraska native was also named that state's Citizen Soldier of the Year in 1989, according to official biographies.

During the 2022 Minnesota governor's race, Walz' opponent accused him of leaving the Guard when he did in order to avoid a deployment to Iraq, though Walz maintained he retired in order to focus on running for Congress, according to the Star Tribune newspaper .

Far-right commentators and media resurfaced those allegations and knocked him for never serving in combat -- something he has never claimed to do -- in contrast with Vance's deployment to Iraq as a combat correspondent.

"Looks like it is time to bring back Swift Boat Veterans for Truth. Oof. Walz is a really unforced error. He bailed on the military when they decided to send him to Iraq. JD Vance actually served," conservative talk radio host Erick Erickson posted on social media Tuesday.

Walz was first elected to the House of Representatives in 2006, becoming the highest-ranking retired enlisted soldier to serve in Congress.

His tenure in Congress included sitting on the House Veterans Affairs Committee, rising to be its ranking member in 2017.

"Walz' leadership on behalf of his fellow veterans when he was in the U.S. House of Representatives is notable at a time when our all-volunteer force continues to struggle to recruit," Allison Jaslow, CEO of Iraq and Afghanistan Veterans of America, said in a statement praising the choice of a veteran to be vice presidential nominee. "How we care for our veterans is as important to our national security as how we care for our troops, and Walz has a record to prove that he understands that imperative."

As the top Democrat on the committee, Walz was a chief adversary for the Trump administration's Department of Veterans Affairs . He battled with then-acting VA Secretary Peter O'Rourke in 2018 during a standoff over O'Rourke's handling of the inspector general's office, and pushed for an investigation into the influence of a trio of informal VA advisers who were members of Trump's Mar-a-Lago club. An investigation by House Democrats completed after Walz left Congress concluded that the so-called Mar-a-Lago trio "violated the law and sought to exert improper influence over government officials to further their own personal interests."

Walz also opposed the Mission Act, the bill that expanded veterans' access to VA-funded care by non-VA doctors that Trump considers one of his signature achievements. Walz said in statements at the time that, while he agreed the program for veterans to seek outside care needed to be fixed, he believed the Mission Act did not have sustainable funding. VA officials in recent years have said community care costs have ballooned following the Mission Act.

Walz supported another bill that Trump touts as a top achievement, the Department of Veterans Affairs Accountability and Whistleblower Protection Act, which sought to make it easier for the VA to fire employees accused of misconduct or poor performance. But the implementation of that law was later part of Walz' fight with O'Rourke . The law also faced legal challenges that prompted the Biden administration to stop using the expedited firing authorities granted by the bill.

Walz was also an early proponent of doing more for veterans exposed to toxins during their military service, sponsored a major veterans suicide prevention bill and advocated for the expansion of GI Bill benefits. And he repeatedly pushed the VA to study marijuana usage to treat PTSD and chronic pain, something that could come up in a future administration if the Department of Justice finalizes reclassifying marijuana into a category of drugs considered less dangerous.

Walz' time in Congress also included a stint on the House Armed Services Committee, a perch he used to advocate for benefits for members of the National Guard .

Walz consistently voted in support of the annual defense policy bill, as well as advocated for repealing the "Don't Ask, Don't Tell" policy that effectively banned gay and lesbian service members.

"He was my battle buddy in the fight to repeal 'Don't Ask, Don't Tell,' and it wouldn't have happened if we didn't have Command Sgt. Maj. Tim Walz helping lead the fight," Murphy said.

Since becoming governor of Minnesota in 2019, Walz' role as commander in chief of the Minnesota National Guard has come under a spotlight several times. In response to a request from the Minneapolis mayor, he activated the Guard in May 2020 to assist law enforcement when some protests over the Minneapolis police killing of George Floyd turned destructive. At the time, Minneapolis' mayor accused Walz of being too slow to order the deployment, a charge he denied.

"It is time to rebuild. Rebuild the city, rebuild our justice system, and rebuild the relationship between law enforcement and those they're charged to protect," Walz said in a statement when he announced the activation.

He also activated the Guard to protect the Minnesota state Capitol in January 2021 amid fears that Trump supporters could riot at state houses like they did at the U.S. Capitol that month. And he's used the Guard for missions that are more routine for the service, such as to help after heavy flooding earlier this summer .

As news broke Tuesday of Walz' selection, he quickly won praise from other Democratic veterans.

"Having a person who wore the uniform and who deployed around the world adds to the ticket someone who can connect with veterans and military families in a way that no one but a veteran can," Jon Soltz, chairman of liberal political action committee VoteVets, said in a statement.

-- Steve Beynon contributed to this story.

Related: Here's Kamala Harris' Record on Veterans and Military Issues

Rebecca Kheel

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19 Facts About Tim Walz, Harris’s Pick for Vice President

Mr. Walz, the governor of Minnesota, worked as a high school social studies teacher and football coach, served in the Army National Guard and chooses Diet Mountain Dew over alcohol.

• Share full article

By Simon J. Levien and Maggie Astor

• Published Aug. 6, 2024 Updated Aug. 9, 2024

Until recently, Gov. Tim Walz of Minnesota was a virtual unknown outside of the Midwest, even among Democrats. But his stock rose fast in the days after President Biden withdrew from the race, clearing a path for Ms. Harris to replace him and pick Mr. Walz as her No. 2.

Here’s a closer look at the Democrats’ new choice for vice president.

1. He is a (very recent) social media darling . Mr. Walz has enjoyed a groundswell of support online from users commenting on his Midwestern “dad vibes” and appealing ordinariness.

2. He started the whole “weird” thing. It was Mr. Walz who labeled former President Donald J. Trump and his running mate, Senator JD Vance of Ohio, “weird” on cable television just a couple of weeks ago. The description soon became a Democratic talking point.

3. He named a highway after Prince and signed the bill in purple ink. “I think we can lay to rest that this is the coolest bill signing we’ll ever do,” he said as he put his name on legislation declaring a stretch of Highway 5 the “Prince Rogers Nelson Memorial Highway” after the musician who had lived in Minnesota.

4. He reminds you of your high school history teacher for a reason. Mr. Walz taught high school social studies and geography — first in Alliance, Neb., and then in Mankato, Minn. — before entering politics.

5. He taught in China in 1989 and speaks some Mandarin. He went to China for a year after graduating from college and taught English there through a program affiliated with Harvard University.

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• ICSE Class 9
• Class 9 Selina Solutions
• Class 9 Maths Concise Selina Solutions
• Chapter 18 Statistics

Concise Selina Solutions for Class 9 Maths Chapter 18- Statistics

The Selina solutions for the questions given in Chapter 18, Statistics, of the Class 9 Selina textbooks are available here. In this chapter students learn about the topic of Statistics in detail. Students can easily score full marks in the exams by solving all the questions present in the Selina textbook.

The Class 9 Selina solutions are very easy to understand. These Class 9 Selina solutions maths cover all the exercise questions included in the book and are according to the syllabus prescribed by the ICSE or CISCE. Here, the PDF of the Class 9 maths Chapter 18 Selina solutions is available which can be downloaded as well as viewed online. Students can also avail these Selina solutions and download it for free to practice them offline as well.

Download PDF of Selina Solutions for Class 9 Maths Chapter 18:- Download Here

Exercise 18(A)

1. State which of the following variables are continuous and which are discrete:

(a) Number of children in your class

(b) Distance travelled by a car

(c) Sizes of shoes

(e) Number of patients in a hospital

(a) Discrete variable.

(b) Continuous variable.

(c) Discrete variable.

(d) Continuous variable.

(e) Discrete variable.

2. Given below are the marks obtained by 30 students in an examination:

Taking class intervals 1 – 10, 11 – 20, ….., 41 – 50; make a frequency table for the above distribution.

The frequency table for the given distribution is

3. The marks of 24 candidates in the subject mathematics are given below:

The maximum marks are 50. Make a frequency distribution taking class intervals 0 – 10, 10-20, …….

In the above frequency distribution, the marks 30 are present in the class of interval 30 – 40 and not in the interval 20 – 30. Similarly, marks 40 are present in the class of interval 40 – 50 and not in 30 – 40.

4. Fill in the blanks:

(a) A quantity which can very from one individual to another is called a ………….

(b) Sizes of shoes are ……….. variables.

(c) Daily temperatures is ……….. variable.

(d) The range of the data 7, 13, 6, 25, 18, 20, 16 is …………

(e) In the class interval 35 – 46; the lower limit is ………. and upper limit is ………

(f) The class mark of class interval 22 – 29 is ………. .

(a) Variable.

(b) Discrete variables.

(c) Continuous variable.

(d) The range is 25 – 6 = 19

(e) Lower limit is 35 and upper limit is 46

(f) The class mark is 22 – 29 = (22 + 29)/2

5. Find the actual lower class limits, upper class limits and the mid-values of the classes: 10 – 19, 20 – 29, 30 – 39 and 40 – 49.

For the class interval: 10 – 19, 

Lower class limit is 10

Upper class limit is 19

So, the mid-value is (10 + 19)/2 = 14.5

For the class interval: 20 – 29,

Lower class limit is 20

Upper class limit is 29

So, the mid-value is (20 + 29)/2 = 24.5

For the class interval: 30 – 39,

Lower class limit is 30

Upper class limit is 39

So, the mid-value is (30 + 39)/2 = 34.5

For the class interval: 40 – 49, 

Lower class limit is 40

Upper class limit is 49

So, the mid-value is (40 + 49)/2 = 44.5

6. Find the actual lower and upper class limits and also the class marks of the classes:

1.1 – 2.0, 2.1 -3.0 and 3.1 – 4.0.

For the class interval: 1.1 – 2.0, 

The lower class limit is 1.1 and the upper class limit is 2.0

Hence, the class mark is (1.1 + 2.0)/2 = 1.55

For the class interval: 2.1 – 3.0 

The lower class limit is 2.1 and the upper class limit is 3.0

Hence, the class mark is (2.1 + 3.0)/2 = 2.55

For the class interval: 3.1 – 4.0

The lower class limit is 3.1 and the upper class limit is 4.0

Hence, the class mark is (3.1 + 4.0)/2 = 3.55

7. Use the table given below to find:

(a) The actual class limits of the fourth class.

(b) The class boundaries of the sixth class.

(c) The class mark of the third class.

(d) The upper and lower limits of the fifth class.

(e) The size of the third class.

(a) The actual class limits of the fourth class will be: 44.5 – 49.5.

(b) The class boundaries of the sixth class will be: 54.5 – 59.5

(c) The class mark of the third class will be the average of the lower limit and the upper limit of the class interval

Hence, the class mark is (40 + 44)/2 = 84/2 = 42

(d) The upper and lower limits of the fifth class are 54 and 50 respectively

(e) The size of the third class is (44 – 40 + 1) = 5

8. Construct a cumulative frequency distribution table from the frequency table given below:

(i)The cumulative frequency distribution table is

(ii)The cumulative frequency distribution table is

9. Construct a frequency distribution table from the following cumulative frequency distribution:

(i)The frequency distribution table is as below:

(ii)The frequency distribution table is as below:

10. Construct a frequency table from the following data:

The frequency table is as below:

11. Construct the frequency distribution table from the following cumulative frequency table:

(i) State the number of students in the age group 10 – 13.

(ii) State the age-group which has the least number of students.

The frequency distribution table is as below:

(i) The number of students in the age group 10 – 13 is 103

(ii) The age group which has the least number of students is 7 – 10

12. Fill in the blanks in the following table:

13. The value of π upto 50 decimal place is

3.14159265358979323846264338327950288419716939937510

(i) Make a frequency distribution table of digits from 0 to 9 after the decimal place.

(ii) Which are the most and least occurring digits?

(i) The frequency distribution table of digits from 0 to 9 after the decimal place is as below:

Most occurring digits are 3 and 9

Least occurring digits are 0

Exercise 18(B)

1. Construct a frequency polygon for the following distribution:

The frequency polygon for the given data is shown below:

Steps for construction:

(i) Draw a histogram for the given data.

(ii) Mark the mid-point at the top of each rectangle of the histogram drawn.

(iii) Also, mark the mid-point of the immediately lower class-interval and mid-point of the immediately higher class-interval.

(iv) Lastly, join the consecutive mid-points marked by straight lines to obtain the required frequency polygon.

2. Construct a combined histogram and frequency polygon for the following frequency distribution:

The combined histogram and frequency polygon for the given data is shown below:

3. Construct a frequency polygon for the following data:

As the class intervals are inclusive, let’s first convert them into the exclusive form.

The frequency polygon for the given data is shown as below:

4. The daily wages in a factory are distributed as follows:

Draw a frequency polygon for this distribution.

5. (i) Draw frequency polygons for each of the following frequency distribution:

(a) using histogram

(b) without using histogram

(a) Using Histogram:

(iv) Lastly, join the consecutive mid-points marked by straight lines to obtain the required frequency polygon. 

(b) Without using Histogram:

(i) Find the class mark (mid-value) of each given class-interval.

Using, Class mark = mid-value = (Upper limit + Lower limit)/2

(ii) On a graph paper, mark class marks along X-axis and frequencies along Y-axis.

(iii) On this graph paper, mark points taking values of class-marks along X-axis and the values of their corresponding frequencies along Y-axis.

(iv) Draw line segments joining the consecutive points marked in step (3) above.

5. (ii) Draw frequency polygons for each of the following frequency distribution:

Selina Solutions for Class 9 Maths Chapter 18- Statistics

The Chapter 18, Statistics, contains 2 exercises and the Solutions given here contains the answers for all the questions present in these exercises. Let us have a look at some of the topics that are being discussed in this chapter.

18.1 Introduction

18.2 Variable

18.3 Tabulation of data

18.4 Frequency

18.5 Frequency distribution table

18.6 Types of frequency distributions

18.7 Class intervals and class limits

18.8 Cumulative frequency and cumulative frequency table

18.9 Graphical representation of data

18.10 Graphical representation of continuous frequency distribution

Statistics is a branch of Mathematics that is concerned with how information is collected, organised, presented, summarised and then analysed so the conclusion may be drawn from the information. Read and learn the Chapter 18 of Selina textbook to get to know more about Statistics. Learn the Selina Solutions for Class 9 effectively to attain excellent result in the examination.

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