Weighted Average

Determine the mean of a numerical data set.

Determine the weighted average of a numerical data set.

6.DS.4 Summarize numerical data sets in relation to their context in multiple ways.

part = percent x whole

5% as a decimal is .05

part = .05 x 60

Part = 3

Add all the data

Divide the sum by the number of data points

The mean of 3,4,5,6,7,8,9

 $\frac{3+4+5+6+7+8+9}{7}=\ mean$  

Sometimes there are data values that hold more importance, or weight, than others within the set.

For example, competitors in a cooking competition are scored in two categories, taste and presentation. The taste category has a higher importance and is worth  60% of the overall score, while the presentation is worth 40% of the overall score.

In this case the data values don't carry the same weight, so a weighted average would be used to find the overall score for each participant.

A baseball player's slugging percentage is a weighted average of the number of singles, doubles, triples, and home runs the player hits out of their total opportunities at bat. Singles have a weight of 1, doubles have a weight of 2, triples have a weight of 3, and home runs have a weight of 4. Therefore, slugging percentage can be calculated with the following formula:

 $slugging\%=\frac{\left(1\cdot S\right)+\left(2\cdot D\right)+\left(3\cdot T\right)+\left(4\cdot H\right)}{no.\ times\ at\ bat}$  

A player had 60 times at bat and had 20 singles, 6 doubles, 1 triple, and 4 home runs. What is the player's slugging percentage?

 $slugging\%=\frac{\left(1\cdot S\right)+\left(2\cdot D\right)+\left(3\cdot T\right)+\left(4\cdot H\right)}{no.\ times\ at\ bat}$  

 $\frac{\left(1\cdot20\right)+\left(2\cdot6\right)+\left(1\cdot3\right)+\left(4\cdot4\right)}{60}$  

 $\frac{\left(1\cdot20\right)+\left(2\cdot6\right)+\left(1\cdot3\right)+\left(4\cdot4\right)}{60}$  

 $\frac{20+12+3+16}{60}$  

 $\frac{51}{60}=0.85\ Slugging\ \%$