Where:

*w*are the weights of each data point_{1}, w_{2}, ..... , w_{n}*x*are the values of each data point_{1}, x_{2}, ..... , x_{n}

e.g: Weighted mean = (2 * 1 + 3 * 2 + 4 * 3) / (2 + 3 + 4) = 11 / 9 = 1.22222

To calculate the weighted mean, you need two sets of data: the values and their corresponding weights. The weighted mean is obtained by multiplying each value by its corresponding weight, summing up these products, and dividing the result by the sum of the weights.

Here's the step-by-step process to calculate the weighted mean:

- Gather the values and their corresponding weights. Let's denote the values as
*x*, and their corresponding weights as w1, w2, w3,..., wn. Ensure that the number of values matches the number of weights._{1}, x_{2}, x_{3},..., x_{n} - Multiply each value by its corresponding weight. Calculate the product of each value and its weight:
*x*._{1}*w_{1}, x_{2}*w_{2}, x_{3}*w_{3},..., x_{n}*w_{n} - Sum up the products. Add up all the products obtained in the previous step:
*(x*._{1}*w1) + (x_{2}*w2) + (x_{3}*w3) + ... + (x_{n}*wn) - Sum up the weights. Calculate the sum of all the weights:
*w*._{1}+ w_{2}+ w_{3}+ ... + w_{n} - Divide the sum of products by the sum of weights. Divide the sum obtained in Step 3 by the sum obtained in Step 4: (x
_{1}*w_{1}+ x_{2}*w_{2}+ x_{3}*w_{3}+ ... + x_{n}*w_{n}) / (w1 + w2 + w3 + ... + wn). - The result of Step 5 is the weighted mean. This value represents the average of the values, taking into account their respective weights.

Here are some additional examples of how the weighted mean can be used:

- To calculate the average salary of a company's employees, where some employees have more experience than others.
- To calculate the average test score of a group of students, where some students have taken more practice tests than others.
- To calculate the average cost of a car, where some cars have more features than others.
- The weighted mean is a powerful tool that can be used to calculate the average of a set of data points, where some data points are more important than others.