Averages & Mixture

Formula of Averages, Mixture and Alligations

 

Averages:average is a number representing an entire set or group of numbers.

Average = Sum of all numbers / numbers of numbers in the set.

Example: average of first ten numbers of two-digit number

(10+11+12+13+14+15+16+17+18+19)/10 =145/10=14.5

• If each number of a set of numbers is increased or decreased by ‘a’then the average of the set of the numbers will also be increased or decreased by ‘a’.
• If each number of a set of numbers is multiplied or divided by ‘a’then the average of the set of the numbers will also be multiplied or divided by ‘a’.

Other easiest way of calculation of average of set of numbers : take an arbitrary number close to set of the numbers (P), then take deviation of all numbers from the arbitrary and sum them(q_!). then average will be P + q_!/n (n = total set of numbers)

Example: seven friends have Rs: 58, 85, 68, 78, 51, 48, 95 with them. find the average Rs have with them,

So take P= 70, so q! = ( -12 + 15 + -2 + 8 + -19 + -22 + 25) = -7.

So average = 70 + (-7/7) = 70 – 1 = 69

 

Average of Mixture:

 

Mixing of two or more quantities of two or more items then,

If p₁ , p₂ , p₃ are three different quantities of q₁, q₂, q₃ item then average will be

 

(p₁q₁ + p₂q₂ + p₃q₃/ p₁ + p₂ + p₃)

Example,

 

Three type of tea A,B & C , quantity of each type of tea 30kg, 25 kg 40kg, and rate per kg as Rs: 150, 180 & 200. What will be average price after mixing?

Tea              weight              rate          amount

A                    30KG               150           4500

B                     25KG               180           4500

C                     45KG               200          9000

Tatal  100 KG                              18000

So average = ( 30x150)+ (25x180) + (45 x 200)/ 30 + 25 + 45 = 18000/100 = 180