# Weighted average

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A weighted average is weighted based on the number of times each value occurs. To calculate a weighted average, you first multiply each value by the number of times it occurs, and then add the products together. After that, you divide by the sum of the number of all the occurrences. For example:

Value:   |   Number of occurrences:
2        |   1
3        |   6
4        |   1
9        |   7
12       |   2
16       |   10


Step 1: $2 \cdot 1+3 \cdot 6+4 \cdot 1+9 \cdot 7+12 \cdot 2+16 \cdot 10=271$

Step 2: $\frac{271}{1 + 6 + 1 + 7 + 2 + 10} = \frac{271}{27}$

Weighted averages can also be calculated if each value has a weight expressed as a percentile, and all the weights add up to 100%. To calculate, you multiply each value by its weight, then add the products up. For example:

Value:   |   Percentage:
2        |   10%
3        |   60%
4        |   5%
9        |  10%
12       |   5%
16       |  10%


Step 1: $2 \cdot 0.1+3\cdot 0.6+4 \cdot 0.05+9 \cdot 0.1+12 \cdot 0.05+16 \cdot 0.1=5.3$