RS Aggarwal Class 9 Chapter 18 Solutions (Mean, Median and Mode of Ungrouped Data)
RS Aggarwal Solutions for Class 9 Maths Chapter 18 will help you understand about Mean, median, and mode of ungrouped data. This chapter of RS Aggarwal Class 9 Maths Solutions will teach you many concepts of this topic where you need to find the arithmetic mean, learn about the properties of arithmetic means, mode and median of ungrouped data, and mean for ungrouped frequency distribution. In the 63 questions spread over 4 exercises, you will get to practice formulas and theorems to find mean, median, mode and average with many different kinds of sums and frequency distributions.
The questions in these chapters are very important for clearing conceptual understanding as well as scoring high in CBSE exams. Our highly skilled faculties have a stronghold on the subject and they provide a solution to each problem in this chapter with lucid explanations. By practising these questions with our solution, you could focus on more important topics and also do a self-assessment on your level of preparation.
You will find the solutions provided by us extremely easy to comprehend as our academic experts solve even the complex ones in the simplest way. You can also get to know the weightage of different topics in order to know which areas have more importance over others and practice them more.
Important Topics for RS Aggarwal Solutions for Class 9 Chapter 18: Mean, median, and mode of Ungrouped Data
The concept of arithmetic mean and average is very commonly used in our daily life when a range of numbers like height of people or ages are given and we need to figure out their mean or average.
- Arithmetic Mean – We can obtain the arithmetic mean of a group of numbers by adding them all up and dividing by the total number of values in that group.
E.g. For the given number 6, 8,2,10, we can find its mean as below:
Mean = (6 + 8 + 2 + 10) / 4 = 6.5
Here n – number of observations
- Properties of Arithmetic Mean – Properties of mean are used to solve different kinds of problems on averages.
Let there be n observations x1, x2, x3, x4, ….., xn, if x is the arithmetic mean then : (x1 – x) + (x2 – x) + (x3 – x) + ……+ (xn – x) = 0
In other words sum of deviations of individual items from their arithmetic mean is 0
- Let there be n observations x1, x2, x3, x4, ….., xn, and x is the arithmetic mean. If each observation is increased by a number a then the new mean of these items would be,(x + a)
- Let there be n observations x1, x2, x3, x4, ….., xn, and x is the arithmetic mean. If each observation is decreased by a number a then the new mean of these items would be,(x + a)
- Let there be n observations x1, x2, x3, x4, ….., xn, and x is the arithmetic mean. If each observation is multiplied by a non zero number a then the new mean of these items would be,(x * a)
- Let there be n observations x1, x2, x3, x4, ….., xn, and x is the arithmetic mean. If each observation is divided by non zero number a then the new mean of these items would be,(x / a)
- If we replace each observation in the arithmetic series by their mean, then the sum of these replaced items is equal to the sum of the specific items.
- Ungrouped and grouped data – Data that is given in individual points is ungrouped data whereas data that is given in intervals is grouped data.
- Frequency distribution – Number of occurrences of distinct values in a data set is its frequency. For a big dataset where it is not possible to find the frequency of data, a frequency distribution table is used which tells us how frequencies are distributed for each data point.
- Mean for ungrouped frequency distribution – Let us see an example of frequency distribution:
|Number of people||Monthly Salary|
In this case to find mean of such an ungrouped data we use the formula:
So in the above table, we get the mean by:
(15 * 5000) + (20 * 10,000) + (8 * 30,000) + (12 * 8000) / 15 + 20 + 8 + 12 = 11,109.09
- Median of ungrouped data – Median is the middle point of an ordered data at the 50 percentile. In an odd number of observations, the median would be the middle value. For an even number of observations, the median is the average of the 2 middle values.
M = (n + 1)/2 ranked value
Here M – median
N – number of observations in ascending order
- Mode of ungrouped data – In an ungrouped data, mode defines that value that occurs the maximum number of times in the data set.
E.g. – Let the data set be 3, 13, 11, 15, 5, 4, 2, 3, 2
Then mode = 2 and 3 as both occur twice in the above data set
Exercise Discussions of RS Aggarwal Solutions for Class 9, Chapter 7: Lines and Angles
- In the first set of RS Aggarwal Solutions for Class 9 Chapter 7, there are 31 questions. These questions need you to find the mean and average of diverse data sets. In some questions, you are given a mean and you would need to figure out the missing values or apply properties of arithmetic mean to solve the questions.
- In the 2nd set of the exercise, there are 14 questions which are mostly on finding mean from frequency distribution table.
- The 3rd set has 10 questions that test your ability to find the median of ungrouped data.
- The 4th set of exercises has 8 questions on the mode of ungrouped data. In some questions, the median is given with a missing value and you have to find the missing value and then the mode.
Benefits of RS Aggarwal Solutions for Class 9, Chapter 18: Mean, median, and mode of Ungrouped Data
Our experts keep in mind the understanding abilities of students of class 9 while formulating solutions to all the questions. They are done step by step and in the course of going through these solutions, you would also learn how to manage your time in a stressful examination environment. The easy method of solving any problem with diagrammatic representations makes out solutions very useful for your exam preparations.