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

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:

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

1. Exercise (Ex 18A) 18.1

2. Exercise (Ex 18B) 18.2

3. Exercise (Ex 18C) 18.3

4. 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 

1. First, go through the chapter thoroughly and cover all the topics.

2. Note down all the important formulae and try to learn them.

3. Start solving the exercise questions without any guidance from anyone.

4. Try the questions at least 3 times if you are unable to solve them.

5. 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.