What is the Difference Between Average and Weighted Average?

The main difference between an average and a weighted average lies in how the values are calculated and the importance assigned to each data point.

• Average: Also known as the arithmetic mean, it is the sum of all values divided by the number of values. It is used to find the median value or average value in a dataset. For example, the average of 5, 4, 1, 2, and 3 is (5+4+1+2+3)/5 = 3.
• Weighted Average: This calculation takes into account the varying degrees of importance or frequency of some factors in a dataset. Each number in the dataset is multiplied by a predetermined weight before the final calculation is made. The weighted average gives more value to items that occur relatively more or have a higher weight assigned to them. For example, if the weights for the numbers in the previous example are 5, 7, 8, 6, and 4, the weighted average would be (55 + 47 + 18 + 26 + 3*4)/30 = 2.83.

In summary:

• An average is the sum of all values divided by the number of values.
• A weighted average is calculated by multiplying each data point by its weight and then dividing the sum by the sum of the weights.

Weighted averages are more commonly used in finance, as they provide a more accurate representation of the data by accounting for the relative importance or frequency of certain factors. Examples of weighted averages in finance include volume-weighted average price (VWAP), weighted average cost of capital (WACC), and portfolio returns.

Comparative Table: Average vs Weighted Average

The main difference between an average and a weighted average is that an average calculates the sum of all values divided by the number of values, while a weighted average takes into account the varying degrees of importance of the values in a dataset. Here is a comparative table highlighting the differences between the two:

For example, to calculate the average of 3, 5, and 8, you would add the numbers and then divide by the total count of added values (3+5+8)/3 = 5.33. To calculate the weighted average, you would multiply each number by its weight and then add the products. For instance, if the weights are 2, 3, and 4, the calculation would be (32 + 53 + 8*4)/(2+3+4) = 5.67.