A weighted average is an average where not all of the pieces of data have the same effect on the outcome. They are, simply put, weighted based on their importance. Weighted averages can be used in any facet to determine an average where your data has different levels of importance. Real estate uses weighted averages for a variety of reasons, particularly to find the appraised value of a home.
Gather your data into a data set. This simply means, have all of your values collected in one location. If you are trying to compute the appraised value of a home, you would want to gather the data of other homes in the area with similar attributes, such as number of bedrooms or bathrooms.
Weight your data. Simply put, this means assign a weight to each piece of data in the set that you just collected. This can either be done by counting how often a piece of data occurs in the set, or you can use a weight based on your own approach. For instance, if you are calculating the average price you paid for a stock and you bought 30 shares at $15 a share and 50 at $18 a share, then your weights would be 30 and 50 respectively. If instead you are computing the average of an appraisal, then you probably would assign a value based on how similar the comparable homes in the area are to the home you are appraising.
Calculate the sum of the weights. The equation to calculate the average when values are weighted is as follows: (X1xW1 + X2xW2 + ... + XnWn) / (W1 + W2 + ... + Wn) Where X1, X2, ..., Xn stands for the values in your data set and W1, W2, ... Wn stand for the weights of each associated x-value. The first step is to sum the weights. If, for example, you are trying to find the right appraised value of a home and you have the following data: House X Value $100,000 - 30 percent weight House Y Value $130,000 - 40 percent weight House Z Value $120,000 - 30 percent weight The sum of the weights would be 30 percent plus 40 percent plus 30 percent, or 100 percent. This value will be used in the final step.
Multiply each x-value by the associated weights. Using the information below, you would find: House X Value $100,000 - 30 percent weight House Y Value $130,000 - 40 percent weight House Z Value $120,000 - 30 percent weight
$100,000 x 30 percent = $30,000 $130,000 x 40 percent = $52,000 $120,000 x 30 percent = $36,000
Add the values found in the previous step. $30,000 + $52,000 + $36,000 = $118,000
Divide the value from the previous step by the sum of the weights found in step three. $118,000 / 100% = $118,000 This is your weighted average. For this example, the value $118,000 indicates the appraised value of the home.
If your final weight is 100 percent, the last step is not necessary. However, the weights are not always percentages, and they do not always add up to 100 percent. Make sure to double check your weights before skipping the last step.