Average: Fundamental Concepts and Qualities I'm going to start a new quantitative aptitude topic today called Average. It is a pretty straightforward subject that only requires basic mathematical computations. The average concept has several uses. In the following session, I will go over its uses. I'll start by trying to explain the fundamentals of this subject to you.
The term "average" simply refers to the mean value of all provided observations, or, alternatively, the arithmetic mean of observations.
Average = (Sum of all observations)/ (Number of observations)
Example1: Calculate the average of the subsequent 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
i) Between the maximum and least observation is the average.
ii) The average will also be multiplied by the same value if the value of each observation is multiplied by some value N. i.e.N.
For example: Assume the prior collection of findings. If all observations are multiplied by 2 then the new observations will be as follows.:
6, 8, 16, 24, 4, 10, 2
New Average Old Average
iii) The average will change by the same amount whether the value of each observation is increased or decreased by some amount.
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
I can therefore state that any general procedure done to observations
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
Example3: The second number in a set of three numbers is twice the first and three times the third. Find the greatest number if the average of these numbers is 44.
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
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
finding the 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)
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 km/hr
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