boitshupoO

2020-10-27

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.

Ian Adams

Skilled2021-04-21Added 163 answers

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 $=(70)/7=10=2(5)=2\times $ 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 $=(20\times 21)/2$

Average $=(20\times 21)(2\times 20)=10.5$

**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

$\Rightarrow (11x)/2=44\times 3\Rightarrow x=24$

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

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 $=((2xy)(x+y))=(2\times (50)\times (56))/(50+56)\Rightarrow 52.83$ km/hr

Eliza Beth13

Skilled2023-05-11Added 130 answers

madeleinejames20

Skilled2023-05-11Added 165 answers

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