Weighted Average

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DEFINITION of 'Weighted Average'

An average in which each quantity to be averaged is assigned a weight. These weightings determine the relative importance of each quantity on the average. Weightings are the equivalent of having that many like items with the same value involved in the average.

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BREAKING DOWN 'Weighted Average'

To demonstrate, let's take the value of letter tiles in the popular game Scrabble.

Value: 10 8 5 4 3 2 1 0
Occurrences: 2 2 1 10 8 7 68 2

To average these values, do a weighted average using the number of occurrences of each value as the weight. To calculate a weighted average:

1. Multiply each value by its weight. (Ans: 20, 16, 5, 40, 24, 14, 68, and 0)
2. Add up the products of value times weight to get the total value. (Ans: Sum=187)
3. Add the weight themselves to get the total weight. (Ans: Sum=100)
4. Divide the total value by the total weight. (Ans: 187/100 = 1.87 = average value of a Scrabble tile)

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