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RS Aggarwal Class 9 Solutions Chapter-18 Mean, Median and Mode of Ungrouped Data

RS Aggarwal Solutions

RS Aggarwal Class 9 Solutions Chapter-18 Mean, Median and Mode of Ungrouped Data

Class 9 RS Aggarwal Chapter-18 Mean, Median and Mode of Ungrouped Data Solutions - Free PDF Download

Vedantu provides the solutions of RS Aggarwal Class 9 Maths Chapter 18. The topic of Chapter 18 of Mathematics is titled Mean, Median, and Mode of ungrouped data. Chapter 18 in Class 9 RS Aggarwal deals with the calculation of mean, median, mode of ungrouped data. The way the solutions are provided by Vedantu is easily understandable. The stepwise solutions of every sum of the chapter give the student an enhanced insight into the chapter.

The measures of central tendency mean median, and mode is used to investigate the various properties of a set of data. A measure of central tendency identifies the center position in a data collection as a single value and uses it to characterize a set of data. It's best described as a tendency for data to cluster around a median value. The three most frequent measures of central tendency in statistics are Mean, Median, and Mode. The optimum central tendency measure relies on the sort of data we have. Let's start by learning what each of these phrases means.

Important Topics RS Aggarwal Solutions Class 9 Maths Chapter 18

In statistics, the three measures of central tendency are mean, median, and mode. While describing a set of data, we identify the core position of any data set. This is referred to as the central tendency measure. Every day, we come across data. We find them in newspapers, articles, bank statements, and phone and electricity bills, among other places. The list goes on and on; they are all around us. The challenge now is if we can deduce certain key characteristics of the data by examining only a subset of the data. The use of measures of central tendency or averages, such as mean, median, and mode, makes this possible.

There are Mainly Two Types of Data

Primary Data - The term "primary data" refers to information obtained by the researcher himself. Data that has already been collected by someone else is referred to as secondary data. Primary data are the data that are collected after conducting surveys, interviews, and extensive research. These data are first-hand sources.

Secondary Data - Secondary data is one of the two main categories of data, with primary data being the other. These two sorts of data are quite valuable in research and statistics. Secondary data are the data collected by someone other than the user.

Now, these data can be presented in 2 ways:

Ungrouped Data: Data that is not categorized after the collection. The first data you collect from an experiment or study is referred to as ungrouped data. The data is unprocessed, meaning it hasn't been categorized, classified, or otherwise grouped. A list of numbers is what an ungrouped piece of data is.

Example: Height of 5 students are 158,160,170,166,166. Find the range of the data given.

Solution: Range = Highest number – lowest number = 170-158 = 12

Grouped Data: Data that is organized in the form of a distribution table is called Grouped Data. Data that has been categorized is referred to as grouped data. This type of data can be displayed using histograms and frequency tables.

For Example:

Class	Frequency
10-20	7
20-30	10
30-40	12
40-50	14
50-60	16

Concept of Grouped Data

Class Interval – 10-20, 20-30, 30-40 are the class intervals.
Lower Limit – The smallest number in the class interval is called the lower limit.

For example: 10 in 10-20, 20 in 20-30.

Upper Limit – The greatest number in the class interval is called the upper limit.

For example: 20 in 10-20, 30 in 20-30.

Class Size – The difference between the smallest and the greatest number in the class interval is called class size.

For Example: Class interval in 19.5 - 9.5 = 19.5 - 9.5 = 10.

Classmark – Midpoint between the class interval.

Class mark = (Lower limit + Upper limit)/2

Measures of Central Tendency

Mean: Mean is the average of all the observations. It is denoted by x̄.

x̄ = x1 + x2 + x3 +...xn/n (ungrouped data)

x̄ = x1f1 + x2f2 +....xnfn/f1 + f2 + ... + fn (grouped data).

Median: Median is the middlemost value from the given set of observations.

Median = (n+1)/2th observation value (if n is odd).

Median = n/2th and (n/2 + 1)th observation value (if n is even).

Mode: The observation that has the maximum frequency is called the Mode.

NCERT Question Based on Mean, Median, and Mode

Q. The following number of goals was scored by a team in a series of 10 matches:m3, 5, 0, 3, 3, 4, 3, 2, 4. Find the mean, median, and mode of these scores.

Solution: Mean = (Sum of all 10 matches) /10 = (2 + 3 + 4 + 5 + 0 + 1 + 3 + 3 + 4 + 3)/10 = 2.8

Median: Arrange the goals in increasing order

0, 1, 2, 3, 3, 3, 3, 4, 4, 5

n = 10 (even)

Median = {(n/2)th observation + (n/2+1)th observation}/2

Median = {5th observation + 6th observation}/2

Median = {3 + 3}/2

Mode: Arrange the goals in increasing order. 0,1,2,3,3,3,3,4,4,5

Since 3 occurs maximum times. Therefore, 3 is the mode.

RS Aggarwal Solutions Class 9 Chapter 18 Exercises

Exercise (Ex 18A) 18.1
Exercise (Ex 18B) 18.2
Exercise (Ex 18C) 18.3
Exercise (Ex 18D)18.4

Statistics: The study that deals with the collection, organization, presentation, analysis, and interpretation of data are called statistics. Statistics is a discipline of applied mathematics that deals with gathering, describing, analyzing, and inferring conclusions from numerical data.

Data: Facts and numbers that are collected for analytical purposes are called Data. A set of facts that includes numbers, words, measurements, observations, and even simple descriptions of things.

Preparation Tips

First, go through the chapter thoroughly and cover all the topics.
Note down all the important formulae and try to learn them.
Start solving the exercise questions without any guidance from anyone.
Try the questions at least 3 times if you are unable to solve them.
Seek help from Vedantu’s solution to check your answers and solve the ones that you were unable to solve.

Conclusion

You can download the PDF of the solutions of Chapter 18 for free from Vedantu. Also, revise and solve the important questions for the Class 9 Maths (RS Aggarwal) exam using the updated CBSE Solutions provided by us. Students can download NCERT Solutions Class 9 Maths to help them to revise the complete Syllabus and score more marks in their examinations.

FAQs on RS Aggarwal Class 9 Solutions Chapter-18 Mean, Median and Mode of Ungrouped Data

1. Why Should I Study RS Aggarwal Solutions Maths Class 9 Chapter 18 (Mean, Median, and Mode of Ungrouped Data) from Vedantu?

The study material of Mean, Median, and Mode of ungrouped data by Vedantu covered all the topics that could be asked for in the course of the examination. The step-by-step solution to every problem helps students to clarify their major doubts. Start studying Vedantu's study material without giving it any second thought. The study material and the solutions are prepared by the CBSE guidelines. The solutions are prepared by the leading educators who have gained expertise in this field over the years. Vedantu gives top priority to its students and helps them to achieve their goals in all possible ways. Vedantu is one of India's most reliable and reliable online coaching institutions.

2. How will Vedantu Help an Average Student to Solve the Questions of RS Aggarwal Solutions Maths Class 9 Chapter 18?

Vedantu caters to students of all merit. Once you enrol in Vedantu, it becomes our duty to strengthen your maths core for solving the most difficult of the sums. The regular classes offered by the platform helps them build an in-depth understanding of the key concepts. Vedantu offers the student the freedom to learn the concepts at their own pace. The notes are prepared after very extensive research so that the students understand the subject well enough to see positive results in their exams. Vedantu helps the student to see learning as a source of enjoyment and not as a burden.

3. What is the difference between Mean and Average according to Class 9 RS Aggarwal Chapter-18 Mean, Median, and Mode of Ungrouped Data Solutions - Free PDF Download?

In everyday life, the term average is frequently used to imply a value that is typical of a group of quantities. A simple example is the average monthly rainfall or the average age of an organization's personnel. "People spend an average of 2 hours per day on social media," we might read in an article. We may deduce from the use of the phrase "average" that not everyone spends 2 hours per day on social media; some spend more, while others spend less.

However, we can deduce from the term average that 2 hours a day is a good estimate of how much time is spent on social media. Even though average and mean are not the same, most people use them interchangeably.

4. How are Mean Median and Mode used in our daily lives?

Mathematics is extremely useful in daily life. Every day, we apply arithmetic principles and skills learned through practicing math problems. Like every other concept in maths, Mean Median and Mode are also used in our daily lives. In the field of healthcare, the terms "mean," "median," and "mode" are used. In the healthcare industry, insurance analysts and actuaries frequently employ the mean, median, and mode. Consider the following scenario: Mean: Insurance analysts frequently analyze the average age of the people for whom they provide insurance to determine the average age of their clients.

5. How to score high in Class 9 Maths?

The only way to do well in math in class 9 is to practice. Complete all of the exercises in each chapter. This will boost your capacity to solve problems as well as your speed and efficiency. Important formulas, definitions, and equations can be written down in a notebook and reviewed regularly. Within a time limit, solve example papers and question papers from past years. This will help you become more comfortable with the paper layout and question types while also improving your time management abilities. Revise frequently so that you can remember everything you've learned for a longer time.