# RS Aggarwal Class 10 Chapter 18 Solutions (Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive)

RS Aggarwal Maths Solutions Class 10 Chapter 18 ‘Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph, and Ogive’ is an extremely helpful guide for you. Chapter 18 of RS Aggarwal Class 10 Maths Solutions deals with the concepts of mean, median, mode and you will also get to learn about cumulative frequency and ogive of grouped and ungrouped data.

RS Aggarwal Maths solutions for Class 10 Chapter 18 has 6 exercises and 92 questions. All these questions cover the major topics of the chapter and are very useful for you to grasp the concepts of the chapter. There is one exercise of multiple-choice questions which includes very short answer questions related to the chapter. Practising all these questions is very important for Class 10 board exams. Questions on mean, median and mode involve various formulae and all of them can be thoroughly memorized with practice.

You can now any time refer to our solutions for RS Aggarwal Class 10 Chapter 18 and clarify all your doubts regarding the chapter. We have solved each question in stepwise format and have ensured that the solutions are as per the latest CBSE Class 10 exam pattern. All our solutions are 100% error-free and easy to access. They will surely help you in receiving better marks in your exams.

## Important topics of RS Aggarwal Class 10 Maths Solutions for Chapter 18: Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive

**Mean**

When a data is given (grouped or ungrouped), then the mean is equal to the sum of observations divided by the total number of observations.

Mean = Sum of observations / Total number of observations

**Mean of Grouped Data when a Class Interval is NOT Given**

Mean = ∑ X_{i}f_{i }/ ∑ f_{i},

Where fi, is the frequency of ith observation of Xi.

**Mean of Grouped Data when a Class Interval is Given**

Mean = ∑ X_{i}f_{i} / ∑ f_{i}

Where fi, is the frequency of ith observation of classmark Xi.

Classmark = X_{1} + X_{2} / 2

Where X_{1} is the lower limit and X_{2} is the upper limit.

**Direct Mean Method**

❖ Arrange the data into the Class intervals and compute the corresponding frequency of each class

❖ Find the corresponding X_{i} by using the formula = lower limits + upper limits / 2

❖ Find the product of X_{i} and f_{i}.

❖ After that calculate the sum [ ∑ X_{i} f_{i} ]

❖ Find the mean with the formula = [ ∑ X_{i} f_{i} ] / ∑ f i

**Assumed Mean Method **

❖ ** **Classify the data into intervals and find the corresponding frequency of each class

❖ Find the corresponding classmark X_{i}.

❖ Take one of X_{i} ‘s as assumed mean and denote it with A.

❖ After this, you have to find the deviation of A from X_{i}‘s,

Deviation, d_{i} = X_{i} – A

❖ Find the mean of the deviations.

❖ Now, find the actual mean using the formula-

Mean = A + ∑ d_{i} X_{i} / ∑ f_{i}

**Step-Deviation Formula **

Mean = A + h x ∑ f_{i} U_{i} / ∑ f_{i}

Where h, is the class width

**Median of Grouped Data when Class Intervals are NOT Given**

❖ The First step is to arrange the data or observations in ascending or descending order.

❖ In the second step, you need to find the cumulative frequencies of each observation and add it to the cumulative frequency column.

❖ If the number of observations is odd, the median is the cumulative frequency just greater than this (n+1)/ 2

❖ If the number of observations is even, the median is the cumulative frequency just greater than this [n/2 + (n/2+1)]/ 2

**Cumulative Frequency and Ogive**

Cumulative Frequency is the frequency obtained by adding all the frequencies up to a certain point. An ogive is a graph that represents the cumulative frequencies. The intersection of ogives of less than type and more than type gives the median of the grouped data.

**Mode**

In grouped data, the observation which has the highest frequency is the mode.

**Relation between Mean, Median, and Mode**

3Median = Mode + 2Mean

### Exercise Discussion of RS Aggarwal Maths Solutions Class 10 Chapter 18: Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive

Exercise 18A

This exercise of RS Aggarwal Solutions for Maths Chapter 18 has 29 questions based on the direct method of finding the mean. These questions are simple as you just need to apply the formula to get the answer.

Exercise 18B

It contains 14 questions about finding the median. You need to use the formulas involved in finding the median.

Exercise 18 C

There are 10 questions in the exercise that are based on the concept of mode when a class interval is given. You need to compute the corresponding mode in these questions.

Exercise 18D

It comprises 7 questions. In these questions, you need to find the mean, median, and mode by the step-deviation method. The questions are quite lengthy, you need to be careful while solving, as you missed any single step then it will be difficult for you to find that mistake.

Exercise 18E

It has 10 questions based on word-problems related to mean, median and mode. All these questions must be practised once you are done with the above exercise.

Exercise 18F

It has 22 questions based on an ogive, less than and more than type ogives, method of finding the median. You need to draw an ogive less than and more than type curves by the corresponding data given in the questions.

### Benefits of RS Aggarwal Maths Solutions Class 10 Chapter 18: Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph, and Ogive by Instasolv

- All your doubts related to RS Aggarwal Class 10 Maths Chapter 18 can be solved easily with the help of our solutions.
- The solutions are easy to understand and written in a stepwise manner with all the formulas used in getting the answers.
- The solutions adhere to the latest CBSE Class 10 board exam syllabus.