CAT Quantitative Aptitude Preparation should include Mean, Mode and Median topics also as it will help you in learning the basics to solve questions in CAT exam. In CAT 2021, a total 34 MCQ and Non-MCQ type questions will be asked from CAT QA section. As compared to the other section, the difficulty level of the CAT Quantitative Aptitude Syllabus is considered more. As per the analysis, candidates attempting at least 26 to 28 questions with 99% accuracy can secure a maximum number of scores in the entrance test.

By analysing CAT previous years questions paper, it can be seen that MCQ type questions had been framed from this topic. Candidates who start CAT Preparation with the understating of basic concepts can easily solve the questions. In this article, the three sections i.e Mean, Median and Mode from the part of Quantitative Aptitude are explained with the formulas and previous years solved questions. Also Check CAT QA Question Paper Analysis

What is Mean?

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

CAT 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

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What is Median? 

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. `

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

CAT 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.

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What is Mode?

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 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 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

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