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Weighted Average Calculator




Note
  • First Enter the values of the numbers seperated by commas whose Weighted average need to be found Example 2,3,4
  • Now enter the weight of these values seperated by commas
  • Click on the calculate button.

Formula used
$\text{Weighted Average} = \frac {w_1 x_1 + w_2 x_2 + w_3 x_3 +..+w_n x_n}{w_1 + w_2 +w_3 +..+w_n}$

Weighted Average Calculator




What is Weighted Average

The weighted average is similar to an ordinary average except that instead of each of the data points contributing equally to the final average, some data points contribute more than others.
So, Average is defined as
$\text{Average} = \frac {x_1 + x_2 + x_3 + ...+ x_n}{n}$
Weighted Average will be defined as
$ \text{Weighted Average} = \frac {w_1 x_1 + w_2 x_2 + w_3 x_3 +..+w_n x_n}{w_1 + w_2 +w_3 +..+w_n}$
Where
$x_1,x_2,..$ are the values
$w_1,w_2,w_3..$ are the weighted given to them
Here we multiply the values with weight and then add them together. Also instead of dividing by the sum of the total number of values, we divide it by the sum of the weights.

Example of Few questions where you can use this Weighted Average formula
    Question 1
    Ravi got 450, 460, 380,490 in Ist, IInd ,IIIrd and IVth of his engineering . The weight of the years are 10,20, 30,40.Calculate the weighted average of the marks on Ravi
    Solution
    Weighted Average is given by
    $ \text{Weighted Average} = \frac {w_1 x_1 + w_2 x_2 + w_3 x_3 +..+w_n x_n}{w_1 + w_2 +w_3 +..+w_n}$
    Where $x_1=450,x_2=460,x_3=380,x_4=490$ and $w_1=10,w_2=20,w_3=30,w_4=40$
    Therefore
    $ \text{Weighted Average} =\frac { 10 \times 450 + 20 \times 460 + 30 \times 380 + 40 \times 490}{10 + 20 + 30 + 40} =447$

    Question 2
    The numbers 80, 36, 20, 55, 70 and 75 have weights 5, 5, 4, 2, 3 and 1 respectively.Calculate the weighted mean?
    Solution
    Weighted Average is given by
    $ \text{Weighted Average} = \frac {w_1 x_1 + w_2 x_2 + w_3 x_3 +..+w_n x_n}{w_1 + w_2 +w_3 +..+w_n}$
    Where $x_1=80,x_2=36,x_3=20,x_4=55,x_5=70,x_6=75$ and $w_1=5,w_2=5,w_3=4,w_4=2,w_5=3,w_6=1$
    Therefore
    $ \text{Weighted Average} =\frac { 5 \times 80 + 5 \times 36 + 4 \times 20 + 2 \times 55 + 3 \times 70 + 1 \times 75 }{5+5+4+2+3+1} =52.75$

How this calculators works

User are request to input the dataset seperated by comma and then also the weight dataset seperated by comma
First Sum of the Number multiplied by Weight is calculated and then we sum of the weight
Then Weighted Average is calculated as
Weighted Average will be defined as
$ \text{Weighted Average} = \frac {w_1 x_1 + w_2 x_2 + w_3 x_3 +..+w_n x_n}{w_1 + w_2 +w_3 +..+w_n}$

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