Value Weighted Average

Arithmetic average is an average in which is defined as the summation of all the given elements divided by the total number of elements. In this all the values get same weighted.

Ex: Find the arithmetic average of 7, 16, 20, 57 and 60.


Arithmetic average = `("sum of all the elements")/("total number of elements")`

sum of all the given elements = 7 + 16 + 20 + 57+ 60 = 160

total number of elements = 5

Arithmetic average = `(160)/(5)`  = 32

so  arithmetic average = 32

In the above example we weighted to all the values.

Weighted average is same as that of arithmetic average but the only difference is that each of the element have assigned different weighted in the data given. The above example changes like that

Ex: Find the weighted  average of 7, 16, 20, 57 and 60, whose occurrences (weighted) values are 4, 3, 6, 2 and 1.

Solution is given after definition and formula

Definition of Weighted Average Value

Weighted average is defined as the summation of the element values multiplied with the occurrences (allocated weighted) which is divided by the summation of the occurrences values. This is called Value Weighted Average.

Formula for the weighted average is given by,

where

`barx_(w) ->`weighted average value

`w_(i) ->`allocated weighted value(occurrences) for the given element.

`x_(i) ->`element value

Steps to calculate weighted average value:

Step 1: Calculate the summation of the element values multiplied with the occurrences (allocated weighted).

Step 2: Calculate the summation of the occurrences values.

Step 3: Now division the value obtain by step 1 with step2 and get weighted average value.

Examples on Weighted Average Value

Ex 1: Find the weighted average of 7, 16, 20, 57 and 60 whose occurrences (weighted) values are 4, 3, 6, 2 and 1.

Sol :    Formula for the weighted average is

Step 1:     `sum_(n=1)^5(w_(i)x_(i))` =  (4) (7) + (3) (16) + (6) (20) + (2) (57) + (1) (60)

= 370

Step 2:         `sum_(n=1)^5 (x_(i))`   =  4 + 3 + 6 + 2 + 1

= 16

Step 3:     weighted average value = `barx_(w)` =   `(370)/(16)`

= 23.125                    Ans

Ex 2: Find the weighted average of 7, 2, 8 and 10, whose occurrences (weighted) values are 3, 2, 1 and 1.

Sol : Formula for the weighted average is

Step 1:   `sum_(n=1)^4(w_(i)x_(i))`  (3) (7) + (2) (2) + (1) (8) + (1) (10)

= 43

Step 2:      `sum_(n=1)^4(w_(i))`  3 + 2 + 1 + 1

= 7

Step 3:       weighted average value = `barx_(w)`   =  `(43)/(7)`

Ans =   6.142