CAT Quantitative Ability Mean, Mode, Median: Check Definitions, Formulas and Previous Year Solved Sample Questions

CAT Quantitative Aptitude preparation requires you to cover topics like Mean, Mode, and Median. These concepts lay the foundation for solving questions in the CAT exam. In CAT 2025, the CAT quantitative ability section will comprise a total of 22 questions, including both Multiple Choice Questions (MCQ) and Non-MCQ types.

CAT quantitative ability mean, mode and median are different ways of representing average of a dataset:

• Mean: Also known as the average, Mean is total numbers divided by total number of values.
• Median: It is the middle value of a dataset in which numbers are arranged in ascending and descending order. 
• Mode: It is the value that appears most frequently in a given set of data. There can be more than one mode in a given dataset. 

This year, the CAT 2025 exam date is scheduled for November 30, 2025. IIM Kozhikode will conduct the exam. The CAT 2025 key dates are:

• CAT 2025 application process: August 1 to September 13, 2025
• CAT 2025 admit card release: November 5, 2025
• CAT 2025 exam: November 30, 2025

Also Read

• CAT Previous Year Question Paper
• CAT Preparation of Quantitative Aptitude
• CAT QA Mock Test

CAT Quantitative Ability 2025 Important Books

CAT preparation not only requires diligent study but you must also take the help of books. Some of the most important CAT QA Books are provided below:

CAT Important Books for Quantitative Ability by Arun Sharma

CAT books for Quantitative Ability by Arun Sharma are the most sought after by the candidates. CAT quantitative aptitude Arun Sharma books are updated with new chapters, topics, exercises, and replica questions along with the approach to answering these questions. Some of the top books and the “Buy” link are provided below:

What is Mean in CAT Quantitative Ability?

Mean is defined as the central tendency that includes a set of data that is used to illustrate the average set of data. This is considered as the primary and the most effective tool for finding out the average in statistics. 

It can also be explained as a midpoint of the dataset. It is determined by adding a set of data and also dividing by monitoring the overall number.

CAT QA Preparation: Important Formulas of Mean

1. Formula of Arithmetic Mean

A= \frac {1}{n} \sum \limits_{i=1}^n a_i

W = weighted average

n = number of terms to be averaged

w_{i} = weights applied to x values

X_{i} = data values to be averaged

2. Formula of Weighted Mean 

W =\frac{\sum_{i=1}^{n} w_{i} X_{i}}{\sum_{i=1}^{n} w_{i}}

W = weighted average

n = number of terms to be averaged

w_{i} = weights applied to x values

X_{i} = data values to be averaged

3. Formula of Harmonic Mean 

Harmonic mean = n / (∑1/x_i)

n – the number of the values in a dataset

x_i – the point in a dataset

Also Read

• CAT Preparation of Quantitative Aptitude
• CAT Preparation 2025
• CAT Quantitative Aptitude Syllabus

CAT 2025 Solved Questions: Mean

Ques. 1: The run score of a batsman is 36,35,50,46,60,55. What is the mean if in 6 innings?

Ans: 36+35+50+46+60+55/6 = 47. 

Ques. 2: A given dataset defines the age of 10 teachers. Their ages are 32,41,28,54,35,26,23,33,38,40. What will be the mean of their age? 

Ans: 32+41+28+54+35+26+23+33+38+40/10 = 35 years

Ques. 3: What is the mean of the first five natural numbers?

Ans: 1+2+3+4+5/5 = 3

Ques. 4: The mean of all 4 digit even natural numbers of the form 'aabb', where a>0, is 

A. 5544 

B. 4466 

C. 4864 

D. 5050 

8: A 

Ques.5. Let A, B and C be three positive integers such that the sum of A and the mean of B and C is 5. In addition, the sum of B and the mean of A and C is 7. Then the sum of A and B is 

A. 6 

B. 4 

C. 7 

D. 5 

6: A

Ques.6. In a group of 10 students, the mean of the lowest 9 scores is 42 while the mean of the highest 9 scores is 47. For the entire group of 10 students, the maximum possible mean exceeds the minimum possible mean by 

A. 5 

B. 3 

C. 4 

D. 6 

3: B

Also Read

• How to solve CAT Quantitative Ability Questions
• Best Android Mobile apps to prepare for CAT 2025
• CAT Online Preparation

What is Median in CAT Quantitative Ability? 

Median is defined as a value or the middle number from a group of number which can be evaluated from that set of data. It is secured after reorganising the data in ascending order. `

What are the Types of Modes in CAT Quantitative Aptitude?

A mode is of three types—bimodal, trimodal, and multimodal. Let us understand them one by one.

• Bimodal: Bimodal refers to ‘two’ modes in a particular data set. When two distinct values or numbers repeat frequently, then that set is called a bimodal data set.

Example: Consider a set {1, 2, 2, 2, 3, 4, 4, 4, 5, 6, 7}. Here, values 2 and 4 are repeating equally, i.e., thrice. Therefore, the given set mode is both 2 and 4, and so, the set is called a bimodal set.

• Trimodal: Trimodal refers to ‘three’ modes in a particular data set. When three distinct values or numbers are repeated frequently and equally, the set is called a trimodal data set.

Example: Consider a set {1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 5, 6}. Here, 1, 2, and 3 are repeating frequently and equally. Therefore, the set is a trimodal set and the mode is 1, 2, and 3.

• Multimodal: In a multimodal set, four or more modes appear in a data set. When 4 or more distinct values are repeated frequently and equally, the set is called a multimodal data set.

Example: Consider a set {1, 1, 2, 2, 3, 3, 4, 4, 5, 6}. Here, 1, 2, 3, and 4 are repeating frequently and equally. Therefore, the mode of the given set is 1, 2, 3, and 4.

CAT QA Preparation: Important Formulas of Median

Med(X) = {X[n/2]/(X[n-1/2]+X[n+1/2]/2)

if n is even

if n is odd

X = ordered list of values in data set

n = number of values in the data set

Also Read

• CAT Verbal Ability & Reading Comprehension Syllabus
• CAT DILR Syllabus

CAT 2025 Solved Questions: Median

Ques. 1: What is the median of 18, 69, and 59?

Ans: Put them in ascending order: 18, 59, 69

The middle number is 59, so the median is 59.

Ques. 2: Where is the median from the following number.

5, 18, 78, 26, 23, 93, 83, 41, 25, 15, 13, 68, 24, 30

Ans: 25

Solutions: After arranging the following numbers in order, we get 

5, 18, 78, 26, 23, 93, 83, 41, 25, 15, 13, 68, 24, 30 

Among the fifteen numbers the middle is eight:

The median value of this set of numbers is 25.

Ques. 3: On a winter vacation, Amit’s family drove through a number of seven states. The oil price is not the same in each state. What will be the median oil cost? Find out the answer from the following numbers. 

1.65, 1.85, 1.90, 1.74, 2.06, 2.10, 2.18

Ans. 1.90 

Solution: After organising the data set we can find 

1.65, 1.74, 1.85, 1.90, 2.06, 2.10, 2.18.

Also Read

• CAT 2025 Seating Arrangement Preparation
• Syllogism for CAT 2025 Logical Reasoning
• CAT Preparation of Venn Diagram for Probability

What is Mode in CAT Quantitative Ability?

The mode can be defined as a value that can be seen in a data set. For instance, If we take X as a discrete random variable, then the value of x will be the mode in which the probability of mass function takes the maximum value. 

CAT 2025 QA Preparation: Important Formula of Mode

L+h(fm-f1)/(fm-f1)+(fm-f2)

where 

L is the lower limit of the modal class.

H is the size of the class interval

fm is the frequency of the modal class

f1 is the frequency of the class preceding the modal class

f2 is the frequency of the class succeeding the modal class

CAT 2025 Solved Questions: Mode

Ques. 1: What is the mode from the following data set

3, 3, 3, 6, 10, 15, 15, 27, 37, 48

Ans: 3

Ques. 2: What is the mode of the following data set

3, 3, 3, 6, 10, 15, 15, 27, 37, 37, 37, 48

Ans: 3 and 37

Ques. 3: What is the mode of the following data set

3, 6, 10, 14, 15, 27, 37, 48

Ans: No mode