Weighted Average

Weighted Average

Lesson Goals

• Determine the mean of a numerical data set.

• Determine the weighted average of a numerical data set.

Standards

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

Multiple Choice

Mrs. Gomez purchased 60 balloons for a party, but when she got home, 5% of the balloons had lost air. Determine how many balloons had lost air by the time she got home.

• 3

• 5

• 6

• 10

To find a percentage

• part = percent x whole

• 5% as a decimal is .05

• part = .05 x 60

• Part = 3

To find the mean:

• Add all the data

• Divide the sum by the number of data points

• The mean of 3,4,5,6,7,8,9

•  $\frac{3+4+5+6+7+8+9}{7}=\ mean$  

Multiple Choice

Mary read six books in January, four books in February, and eight books in March.What was the average number of books read each month? __________

• 18
• 6
• 14

Weighted Average

• 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.

Find a Weighted Average

• At Tuhey Pool on June 10th 60% of the swimmers were girls, 40% were boys.

• If the average age of the girls was 14 and the average age of the boys was 12, what is the average age of all swimmers on June 10th?

Find a Weighted Average

• Girls: 60% avg age of 14

• Boys: 40% avg age of 12

• To find the weighted average

• (.6x14) + (.4x12)

• (8.4) + (4.8) = 13.2 avg age of swimmers

Find the Weighted Average

• 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:

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

Find the Weighted Average

• 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?
  

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

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

Find the weighted average

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

•  $\frac{20+12+3+16}{60}$  

•  $\frac{51}{60}=0.85\ Slugging\ \%$