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# Weighted Mean Calculator

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Weighted mean calculator helps to calculate the weighted mean of a set a data. These data are the weights with their values of the data. The formula to calculate the weighted mean is given as,

Weighted mean = $\frac{w_{1}x_{1} + w_{2}x_{2} + .......w_{n} x_{n}}{w_{1} + w_{2} + ......w_{n}}$

Where,
{$w_{1}$, $w_{2}$, $w_{3}$,....$w_{n}$} = respective weights of the data,
{$x_{1}$, $x_{2}$, $x_{3}$,......$x_{n}$} = values of the data.

## Steps

Step 1 : Jot down the weights and values of the data from the problem.

Step 2 : Find the weighted mean of the given data by substituting the values into the formula,
Weighted mean = $\frac{w_{1}x_{1} + w_{2}x_{2} + .......w_{n} x_{n}}{w_{1} + w_{2} + ......w_{n}}$.

## Problems

Given below are some of the problems related to weighted mean.

### Solved Examples

Question 1: The numbers 5, 2, 3, and 6 have weights 20, 15, 22 and 30. Determine the weighted mean of the data.
Solution:

Given range : $x_1$ = 5, $x_2$ = 2, $x_3$ = 3, $x_4$ = 6

Given weights : $w_{1}$ = 20, $w_{2}$ = 15, $w_{3}$ = 22, $x_{4}$ = 30

Weighted mean of the given data is,

Weighted mean = $\frac{w_{1}x_{1} + w_{2}x_{2} + w_{3}x_{3} + w_{4}x_{4}}{w_{1} + w_{2} + w_{3} + w_{4}}$

Weighted mean = $\frac{20 \times 5 + 15 \times 2 + 22 \times 3 + 30 \times 6}{20 + 15 + 22 + 30}$

Weighted mean = $\frac{376}{87}$

Weighted mean = 4.32

Question 2: The numbers 1, 2, 3, 4 and 5 have weights 30, 40, 20, 10 and 50. Determine the weighted mean of the data.
Solution:

Given range : $x_1$ = 1, $x_2$ = 2, $x_3$ = 3, $x_4$ = 4 , $x_5$ = 5

Given weights : $w_{1}$ = 30, $w_{2}$ = 40, $w_{3}$ = 20, $x_{4}$ = 10, $x_5$ = 50

Weighted mean of the given data is,

Weighted mean = $\frac{w_{1}x_{1} + w_{2}x_{2} + w_{3}x_{3} + w_{4}x_{4} + w_{5}x_{5}}{w_{1} + w_{2} + w_{3} + w_{4} + w_{5}}$

Weighted mean = $\frac{30 \times 1 + 40 \times 2 + 20 \times 3 + 10 \times 4 + 50 \times 5}{30 + 40 + 20 + 10 + 50}$

Weighted mean = $\frac{460}{150}$

Weighted mean = 3.06