Ask question

# Average: Basic Understanding and Properties Today I'm going to start a new topic of quantitative aptitude i.e. Average. It is a very simple topic and just involves simple mathematical calculations. Average concept has various applications. I will discuss its applications in next session. Firstly I will try to make you understand the basics of this topic.

Question
Polynomial factorization
asked 2020-10-27
Average: Basic Understanding and Properties Today I'm going to start a new topic of quantitative aptitude i.e. Average. It is a very simple topic and just involves simple mathematical calculations. Average concept has various applications. I will discuss its applications in next session. Firstly I will try to make you understand the basics of this topic.

## Answers (1)

2021-04-21

Average is just a mean value of all the given observation or i can say it is an arithmetic mean of observations.

Average = (Sum of all observations)/ (Number of observations)

Example1: Find an average of  following observations:

3, 4, 8, 12, 2, 5, 1

Solution: Average = (Sum of all observations)/ (Number of observations)

Average = (3+ 4+ 8+ 12 +2+ 5+ 1)/7 = 35/7 = 5

So, Average = 5

***But, remember that this formula does not directly applies on average speed. Discussed in special cases***

## Properties of Average

i) Average lies between maximum and minimum observation.
ii) If value of each observation is multiplied by some value N, then average will also be multiplied by the same value i.e.N.
For example: Assume the previous set of observations. If 2 is multiplied with all observations, then new observations will be as follows:
6, 8, 16, 24, 4, 10, 2
New Average = (70)/7 = 10 = 2(5) = 2 times Old Average
iii) If value of each observation is increased or decreased by some number, then average will also be increased or decreased by the same number.
For example: Continuing with the same example. If 2 is added to all observations, then new observations will be as follows:
5, 6, 10, 14, 4, 7, 3
New Average = (49)/7 = 7 = (5 + 2) = 2 + Old Average
iv) Similarly, if each observation is divided by some number, then average will also be divided by same number.
For example: If 2 is divided from all observations, then new observations will be as follows:
1.5, 2, 4, 6, 1, 2.5, 0.5
New Average = (17.5)/7 = 2.5 = 5/2 =  Old Average/ 2
Therefore, I can say any general operation applied on observations will have same effect on average.
Example2: Find an average of first 20 natural numbers.
Solution: Average =(Sum of first  20  natural numbers)/ (20)
Now, we know that Sum of first n natural numbers = ((n)(n+1))/2
Therefore, Sum of first 20 natural numbers = (20 times 21)/2
Average = (20 times 21)(2 times 20) = 10.5
Example3: Out of three numbers, second number is twice the first and is also thrice the third. If average of these numbers if 44, then find the largest number.
Solution: Let x be the third number
According to question, second number = 3x = 2(first number)
Therefore, first number = (3x)/2 second number = 3x and third number = x
Now, average = 44 = (x + 3x + (3x)/2)/3
⇒(11x)/2 = 44 times 3 ⇒x = 24
So, largest number i.e. (3x) = 72
Example4: Average of four consecutive even numbers is 27. Find the numbers.
Solution: Let x, x+2, x+4 and x+6 be the four consecutive even numbers.
According to question, ((x) + (x+2) + (x+4) + (x+6))/4 = 27
(4x + 120)/4 = 27 x = 24 Therefore, numbers are 24, 26, 28, 30

## Special Case

### To find average speed

Suppose a man covers a certain distance at x km/hr and covers an equal distance at y km/hr. The average speed during the whole distance covered will be (2xy)/ (x+y)
*I will soon update a video lesson of this concept that how this formula has been derived.*
Example5: A bike covers certain distance from A to B at 50 km/hr speed and returns back to A at 56 km/hr. Find the average speed of the bike during the whole journey.

Solution: Average speed = ((2xy)(x+y)) = (2 times (50) times (56))/ (50 + 56)
⇒ 52.83 km/hr

### Relevant Questions

asked 2020-11-30
Geometry -concepts and properties for SSC CGL Tier-I Geometry is one of the most important topics of Quantitative Aptitude section of SSC CGL exam. It includes various concepts related to lines, angles, triangles, circles, polygons and so on. So, today I will just discuss concept and properties of triangle. Always remember that in Geometry, You need a very basic understanding. Cramming is not gonna help you anywhere.
asked 2021-02-02
Tricks to solve problems related to Series in Quantitative Aptitude Today, I'm going to discuss a very important topic of Quantitative aptitude i.e. Sequence and Series. Sequence and Series is a mathematical concept and basically it is a logical concept.
asked 2020-11-22
Time and Work: Techniques and examples with solutions Today I'm going to discuss a very important topic i.e. Time and Work of quantitative aptitude. In almost every exam at least 2-3 question are asked every time. In this chapter, I will tell you about a definite relationship between Time and work and easy method to solve the problems.
asked 2021-03-07
Solved examples of number series in Quantitative aptitude As we know, questions related to number series are very important in Quantitative aptitude section, So, today I’m going to discuss some problems of number series. These are just for your practice. I have already discussed this chapter in previous session i.e. Sequence and Series. Read this article first, then go through these examples.
asked 2021-02-04
Basic facts and techniques of Boats and Streams of Quantitative Aptitude Boats and Streams is a part of the Quantitative aptitude section. This is just a logical extension of motion in a straight line. One or two questions are asked from this chapter in almost every exam. Today I will tell you some important facts and terminologies which will help you to make better understanding about this topic.
asked 2021-02-19
Simple or linear Equations: Tricks and Examples. I have already discussed a concept - Quadratic Equations of quantitative aptitude. Today I will discuss some examples of simple equations which have been proved to be a very important topic for various competitive exams. The problems of linear equations can be easily solved by using simple tricks. Lets discuss how.
asked 2021-02-26
The top string of a guitar has a fundamental frequency of 33O Hz when it is allowed to vibrate as a whole, along all its 64.0-cm length from the neck to the bridge. A fret is provided for limiting vibration to just the lower two thirds of the string, If the string is pressed down at this fret and plucked, what is the new fundamental frequency? The guitarist can play a "natural harmonic" by gently touching the string at the location of this fret and plucking the string at about one sixth of the way along its length from the bridge. What frequency will be heard then?
asked 2021-01-04
Important Questions of Mensuration: Quantitative Aptitude Mensuration is one the toughest topic of quantitative aptitude section. The only thing is it takes time to analyze the question. Rest is just clarification and formula learning ability of candidate. This chapter is a part of quantitative aptitude section of SSC CGL and SBI PO. Today I will discuss some questions related to basic terms of mensuration.
asked 2021-01-31
Tricks to solve Ratio and Proportion Problems Today I'm going to discuss a very helpful trick of ratio and proportion of Quantitative Aptitude section. I'm sure this would be very helpful for you and this trick will save your more than half time, you generally take to solve the question.
asked 2021-02-25
We will now add support for register-memory ALU operations to the classic five-stage RISC pipeline. To offset this increase in complexity, all memory addressing will be restricted to register indirect (i.e., all addresses are simply a value held in a register; no offset or displacement may be added to the register value). For example, the register-memory instruction add x4, x5, (x1) means add the contents of register x5 to the contents of the memory location with address equal to the value in register x1 and put the sum in register x4. Register-register ALU operations are unchanged. The following items apply to the integer RISC pipeline:
a. List a rearranged order of the five traditional stages of the RISC pipeline that will support register-memory operations implemented exclusively by register indirect addressing.
b. Describe what new forwarding paths are needed for the rearranged pipeline by stating the source, destination, and information transferred on each needed new path.
c. For the reordered stages of the RISC pipeline, what new data hazards are created by this addressing mode? Give an instruction sequence illustrating each new hazard.
d. List all of the ways that the RISC pipeline with register-memory ALU operations can have a different instruction count for a given program than the original RISC pipeline. Give a pair of specific instruction sequences, one for the original pipeline and one for the rearranged pipeline, to illustrate each way.
Hint for (d): Give a pair of instruction sequences where the RISC pipeline has “more” instructions than the reg-mem architecture. Also give a pair of instruction sequences where the RISC pipeline has “fewer” instructions than the reg-mem architecture.
...