Average

 Average

We have divide Average in 4 types:

[A] Arithmetic Mean

[B] Weighted Arithmetic Mean

[C] Harmonic Mean (Speed)

[D] Weighted Harmonic Mean (Speed)

[A] Arithmetic Mean :

Example : Find the average of 12, 15, 18, 20 & 27.

[B] Weighted Arithmetic Mean :

Example : A class has 50 boys & 100 girls. The average marks obtain by boys are 70 & that of girls are 55. Find the average marks obtain by the all class.

x1 = 70

x2 = 55

n1 = 50

n2 = 100

Average = [(50*70) + (100*55)] / (100+50)

              = (3500 + 5500) / 150

              = 9000 / 150

              = 60

So, we can say that average marks obtain by the all class is 60.

[C] Harmonic Mean (Speed) :

 Same Distance and Different speed between 2 stations.

Average Speed = 2ab / (a+b)

Example : Mr. A travel from Rajkot to Junagadh at a speed of 30 km/hr and return back from Junagadh to Rajkot at a speed of 20 km/hr. Find His average speed during the all Jurney.

Average speed = 2ab / (a+b)

                        = (2*30*20) / (30+20)

                        = 1200 / 50

                        = 24.

[D] Weighted Harmonic Mean (Speed) :

Same Distance and Different speed in more than 2 stations.

Example : A person Travel from A to B at a speed of 30 km/hr, B to C at a speed of 20 km/hr, C to D at a speed of 15 km/hr and D to E at a speed of 10 km/hr. If all the cities are at equal distance then find average speed. 

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Questions :

Example : Find the average of first 7 prime Number .

Solution : Average = (2+3+5+7+11+13+17) / 7

                               = 58 / 7 

                               = 8.28

Example :  A Student Bought 4 Books for Rupees 120 from 1 Book store and 6 books for rupees 150 from another book store . Find the average price. He paid the book store.

Solution : 

120 rupees  = 4 books

150 rupees  = 6 books

average = (120+150) / (4+6)

             = 270 / 10

             = 27 

Example : Average Monthly income of a family of 4 earning members was rupees 2940. One of the earning member died and there for the average income came down to rupees 2600. Find the income of the died member :

 Solution : 

member = 4   , Average Income = 2940 

So, Total Income  = 2940 * 4 = 11760

member = 3   , Average Income = 2600

So, Total Income  = 2600 * 3 = 7800

So, Income of died member = 11760 - 7800 = 3960.