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.

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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