What is a weighted average?
A weighted average is a method of computing an arithmetic mean of a set of numbers in which some elements of the set carry more importance than others. As an example, grades are generally calculated using a weighted average. Consider the following scenario:
If Andy has a homework grade of 92, a quiz grade of 68 and a unit test grade of 81, then his overall grade would equal:
(.10)(92) + (.20)(68) + (.70)(81) = 79.5
On-line grade calculator
The National Hockey League (NHL) utilizes a team points system to determine league standings. A win is worth 2 points and a loss after regulation play (overtime or shootouts) is worth 1 point. Losses in regulation play are worth 0 points. How many points would a team have if they had 33 wins, 17 losses during regulation and 10 losses after regulation play?
2 teams finish the regular season tied for 1st place in their division. Your job as NHL commissioner is to choose the division champion.
Team A finishes the season with: 41 wins, 28 losses, 13 overtime losses = 95 points
Team B finishes the season with: 38 wins, 25 losses, 19 overtime losses = 95 points
Which team do you choose and why?
Assignment
1. Complete the Google Docs worksheet.
2. Grade calculation assignment (Weighted Index)
Quarterback rating
Since 1960 the National Football League (NFL) rates quarterbacks for statistical purposes against a fixed performance standard based on the statistical achievements of all qualified quarterbacks in the league. This system allows passing performances to be compared from one year to the next. In the 2013-14 season, Peyton Manning set an NFL record with 55 touchdown (TD) passes and led the Denver Broncos to the Super Bowl. Calculate his QB rating based on the statistics below.
Completions (450) Attempts (659) Completion % (68.3) TD (55) Int (10) Yards(5477)
A weighted average is a method of computing an arithmetic mean of a set of numbers in which some elements of the set carry more importance than others. As an example, grades are generally calculated using a weighted average. Consider the following scenario:
- Homework counts 10%
- Quizzes count 20%
- Unit tests count 70%
If Andy has a homework grade of 92, a quiz grade of 68 and a unit test grade of 81, then his overall grade would equal:
(.10)(92) + (.20)(68) + (.70)(81) = 79.5
On-line grade calculator
The National Hockey League (NHL) utilizes a team points system to determine league standings. A win is worth 2 points and a loss after regulation play (overtime or shootouts) is worth 1 point. Losses in regulation play are worth 0 points. How many points would a team have if they had 33 wins, 17 losses during regulation and 10 losses after regulation play?
2 teams finish the regular season tied for 1st place in their division. Your job as NHL commissioner is to choose the division champion.
Team A finishes the season with: 41 wins, 28 losses, 13 overtime losses = 95 points
Team B finishes the season with: 38 wins, 25 losses, 19 overtime losses = 95 points
Which team do you choose and why?
Assignment
1. Complete the Google Docs worksheet.
2. Grade calculation assignment (Weighted Index)
Quarterback rating
Since 1960 the National Football League (NFL) rates quarterbacks for statistical purposes against a fixed performance standard based on the statistical achievements of all qualified quarterbacks in the league. This system allows passing performances to be compared from one year to the next. In the 2013-14 season, Peyton Manning set an NFL record with 55 touchdown (TD) passes and led the Denver Broncos to the Super Bowl. Calculate his QB rating based on the statistics below.
Completions (450) Attempts (659) Completion % (68.3) TD (55) Int (10) Yards(5477)
Tom Brady, Matt Ryan, Drew Brees and Aaron Rodgers are considered to be the top 4 quarterbacks in the NFL. Determine quarterback ratings for their career (including postseason) and how many Super Bowl championships their teams have won. Click on this link to find their career stats from nfl.com. Based on your calculations, complete the survey below.
QB rating survey
Reflection
An index is numerical scale that can be used to give general information about general trends, compare variables and help make comparisons and judgments. It is often calculated as a weighted sum of various factors resulting in a single summary number. How can the quarterback rating system be thought of as an index?
Slugging percentage
Another example of weighted average in sports is a baseball player's slugging percentage. In 2001, Barry Bonds broke an 81 year old record held by Babe Ruth by finishing the season with a slugging percentage of .863. Determine the slugging percentage for LA Angels center fielder Mike Trout based on his stats from the 2013-14 season.
Total AB (589) Hits (190) 2B (39) 3B (9) HR (27) SAC (9) HBP (8) Walks (110)
Use the interactive tool to view and compare the slugging percentage of some of the top players in major league baseball to Mike Trout's slugging percentage. What do the graphs tell you about the consistency, or inconsistency, of each player's hitting ability?
Reflection
Is it possible to have a slugging percentage of more than 1? Theoretically, what is the highest possible value for a slugging percentage? Is it realistic for a player to ever achieve this over an entire baseball season? Based on statistics and research, what do you consider to be a good slugging percentage? Discuss some other weighted averages/measures that are currently be used in Major League Baseball to quantify the value of different position players.
QB rating survey
Reflection
An index is numerical scale that can be used to give general information about general trends, compare variables and help make comparisons and judgments. It is often calculated as a weighted sum of various factors resulting in a single summary number. How can the quarterback rating system be thought of as an index?
Slugging percentage
Another example of weighted average in sports is a baseball player's slugging percentage. In 2001, Barry Bonds broke an 81 year old record held by Babe Ruth by finishing the season with a slugging percentage of .863. Determine the slugging percentage for LA Angels center fielder Mike Trout based on his stats from the 2013-14 season.
Total AB (589) Hits (190) 2B (39) 3B (9) HR (27) SAC (9) HBP (8) Walks (110)
Use the interactive tool to view and compare the slugging percentage of some of the top players in major league baseball to Mike Trout's slugging percentage. What do the graphs tell you about the consistency, or inconsistency, of each player's hitting ability?
Reflection
Is it possible to have a slugging percentage of more than 1? Theoretically, what is the highest possible value for a slugging percentage? Is it realistic for a player to ever achieve this over an entire baseball season? Based on statistics and research, what do you consider to be a good slugging percentage? Discuss some other weighted averages/measures that are currently be used in Major League Baseball to quantify the value of different position players.
Class assignment - Weighted averages
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Flesch-Kincaid readability index
The Flesch-Kincaid Index is a good tool for writers or marketing personnel. It is a simple way to measure the level of reading ease (readability index) or difficulty for any piece of writing. The formula considers the average number of words per sentence (average sentence length) and the average number of syllables per word within a given passage in order to estimate the complexity of the text. The formula then converts that complexity level into a score that roughly equates with a grade level K-12 (University of South Florida). The index does not determine if a writing is too basic or too advanced for the reader but rather is a mathematic calculation of the ease or difficulty of reading. The index reflects the equivalent of reading grade level.
Reflection
Have you ever received mail advertising a product you might be interested in purchasing? Did the ad contain a lot of text? Did you read everything in the ad? As the marketing director for a company, do you think it is important to determine the readability level of prospective customers?
How is the Flesch-Kincaid Index calculated?
Flesch-Kincaid index calculation
Online readability calculator
Assignment
Find the Flesch-Kincaid Index for the Gettysburg Address using the 3 methods indicated below:
Compare your results. Do you consider the Flesch-Kincaid Index to be a precise measurement of how easy or difficult material is to read? Support your answers with research. Compare and contrast the Flesch-Kincaid Index with the Fog Index.
The Flesch-Kincaid Index is a good tool for writers or marketing personnel. It is a simple way to measure the level of reading ease (readability index) or difficulty for any piece of writing. The formula considers the average number of words per sentence (average sentence length) and the average number of syllables per word within a given passage in order to estimate the complexity of the text. The formula then converts that complexity level into a score that roughly equates with a grade level K-12 (University of South Florida). The index does not determine if a writing is too basic or too advanced for the reader but rather is a mathematic calculation of the ease or difficulty of reading. The index reflects the equivalent of reading grade level.
Reflection
Have you ever received mail advertising a product you might be interested in purchasing? Did the ad contain a lot of text? Did you read everything in the ad? As the marketing director for a company, do you think it is important to determine the readability level of prospective customers?
How is the Flesch-Kincaid Index calculated?
Flesch-Kincaid index calculation
Online readability calculator
Assignment
Find the Flesch-Kincaid Index for the Gettysburg Address using the 3 methods indicated below:
- index formula
- copy and paste the document into the online readability index calculator
- copy and paste the document into Microsoft Word and follow the directions listed below
Compare your results. Do you consider the Flesch-Kincaid Index to be a precise measurement of how easy or difficult material is to read? Support your answers with research. Compare and contrast the Flesch-Kincaid Index with the Fog Index.