Weighted Average

The weighted average is a type of average that takes into account the relative importance of each data point. It is calculated by multiplying each data point by its weight, and then adding the results together and dividing by the total weight.

For example, let's say you have three test scores: 90, 80, and 70. The unweighted average of these scores is 80. However, if you know that the first test was worth twice as much as the second test, and the second test was worth twice as much as the third test, then the weighted average would be 85.

The weighted average is often used in finance to calculate the return on an investment. For example, if you invest $100 in a stock that goes up 10% and $200 in a stock that goes up 20%, the unweighted average return would be 15%. However, the weighted average return would be 17.5%, because the $200 investment is worth more than the $100 investment.

The weighted average is also used in statistics to calculate the mean of a set of data. The mean is the average value of the data points, and it is calculated by adding all of the data points together and dividing by the number of data points. However, if the data points are not all equally important, then the weighted mean is a more accurate representation of the data set.

The weighted mean is calculated by multiplying each data point by its weight, and then adding the results together and dividing by the total weight. The weights can be any number, but they must be positive and they must add up to 1.

The weighted mean is a useful tool for summarizing data sets that are not all equally important. It is also a more accurate representation of the data set than the unweighted mean.