Weighted Average

What Is a Weighted Average?

A weighted average is a type of arithmetic mean in which some values count more heavily than others. Instead of giving every number the same influence, each value is multiplied by a weight, and the sum of those products is divided by the total of the weights. Weights usually reflect size, quantity, or importance, so the result leans toward the values that carry the most weight.

How It Is Calculated

The general formula is:

Weighted average = (w1 × x1 + w2 × x2 + ... + wn × xn) ÷ (w1 + w2 + ... + wn)

Here, each x is a value and each w is its weight. If the weights already add up to 1 (or 100%), the division step can be skipped and the result is simply the sum of the weighted values.

An Example

Suppose an investor buys 100 shares of a stock at $20 and later buys 300 more at $30. A simple average of the two prices is $25, but that ignores how many shares were bought at each price. Using share counts as the weights gives:

(100 × $20 + 300 × $30) ÷ 400 = $27.50

Because three-quarters of the shares were bought at $30, the result sits closer to that price. This same logic underlies a cost basis calculation that some investors use to track the average purchase price of shares they hold.

Why It Matters to Investors

Weighted averages appear throughout investing and finance. Many stock market indexes, such as the S&P 500, weight each company by its market capitalization, so larger companies have more influence on the index value. The Dow Jones Industrial Average, by contrast, is a price-weighted index, meaning higher-priced stocks move it more. Companies also use a weighted average cost of capital to estimate the blended cost of their debt and equity financing.

Knowing how a weighting method works helps explain why an index or average may move differently from a simple count of its members.

Limitations

A weighted average is only as meaningful as the weights behind it. Choosing different weights can change the result considerably, and the average alone does not show how widely the individual values are spread. Weights also need to be measured consistently, since mixing time periods or units can produce misleading figures.