Mean, Median, Mode, Range & Outlier

Vocabulary Mean Median Mode Range Outlier

the sum of the data divided by the total number of elements 2, 5, 7, 8, 5, 9, 3, 4, 8, 5, 6, 9, 10, 20, 6, 5, 4, 8, 4, 2 Mean (average) the sum of the data divided by the total number of elements 2+5+7+8+5+9+3+4+8+5+6+9+10+20+6+5+4+8+4+2 = 130 130 ÷ 20 = 6.5

DATA: 2, 5, 7, 8, 5, 9, 3, 4, 8, 5, 6, 9, 10, 20, 6, 5, 4, 8, 4, 2 Median (middle) The middle number in an ordered set of data (or average of middle 2 numbers) 2, 2, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 7, 8, 8, 8, 9, 9, 10, 20 5 + 6 = 11 11 ÷ 2 = 5.5

Easiest way to see is to put them in order…. DATA: 2, 5, 7, 8, 5, 9, 3, 4, 8, 5, 6, 9, 10, 20, 6, 5, 4, 8, 4, 2 Mode (most) The number that occurs the most times in a set of data (could be multiple modes or no mode) Easiest way to see is to put them in order…. 2, 2, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 7, 8, 8, 8, 9, 9, 10, 20

Range (difference) DATA: 2, 5, 7, 8, 5, 9, 3, 4, 8, 5, 6, 9, 10, 20, 6, 5, 4, 8, 4, 2 Range (difference) The difference between the highest and lowest value in a set of data Easiest way to see is to put them in order…. 2, 2, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 7, 8, 8, 8, 9, 9, 10, 20 20 – 2 = 18

Easiest way to see is to put them in order…. DATA: 2, 5, 7, 8, 5, 9, 3, 4, 8, 5, 6, 9, 10, 20, 6, 5, 4, 8, 4, 2 Outlier A number that is much different than the test of the numbers. May skew the measurements Easiest way to see is to put them in order…. 2, 2, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 7, 8, 8, 8, 9, 9, 10, 20

Example World’s Richest Athletes 2016 Rank Name Sport Nation Total in millions 1 Soccer Portugal $88 2 Argentina $81 3 Basketball United States $77 4 Tennis Switzerland $68 5 $56 6 Serbia 7 Football $53 8 Golf 9 10 $50 Cristiano Ronaldo Lionel Messi LeBron James Roger Federer Kevin Durant Novak Djokovic Cam Newton Phil Mickelson Jordan Spieth Kobe Bryant

Mean Median Mode Range World’s Richest Athletes 2016 Add the numbers and divide by the number of elements $88 $81 $77 $68 $56 $53 $50 Mean = 63.3 Median The middle number when the numbers are placed in order 50 53 53 53 56 56 68 77 81 88 Median= 56 Mode The number that appears the most Mode= 53 Range The difference between the greatest and smallest number Range = 38

Example World’s Most Popular Sports Rank Name Where watched Total in millions 1 Europe, Africa, Asia, America 3,500 2 Asia, Australia, UK 2,500 3 US, Canada, China, Phillipines 2,200 4 Europe, Africa, Asia, Australia 2,000 5 Europe, Americas, Asia 1,000 6 Asia, Europe, Americas, Australia 900 7 Asia, Europe, Africa, Americas 850 8 US, Japan, Cuba, Dominican Republic 500 9 United States 410 10 France, England, New Zealand, South Africa 11 Europe, Asia, America, Canada 390 Football (Soccer) Cricket Basketball Field Hockey Tennis Volleyball Table Tennis Baseball American Football Rugby Golf

Mean Median Mode Range World’s Most Popular Sports Add the numbers and divide by the number of elements 3,500 2,500 2,200 2,000 1,000 900 850 500 410 390 Mean = 1333 Median The middle number when the numbers are placed in order 390 410 410 500 850 900 1000 2000 2200 2500 3500 Median= 900 Mode The number that appears the most Mode= 410 Range The difference between the greatest and smallest number Range = 3110

These are the scores from a math test: 90, 94, 53, 68, 79, 84, 87, 72, 70, 69, 65, 89, 85, 83, 72 You earned a score of 79. Your mom asks you how you did on the test compared to the rest of the class.

Your score: 79 Mean: 1164 / 15 = 77.6 Median: 79 Mode: 72 Numerical Order: 53, 65, 68, 69, 72, 72, 72, 79, 83, 84, 85, 89, 89, 90, 94 Your score: 79 Mean: 1164 / 15 = 77.6 Median: 79 Mode: 72

Which describes the data better – mean, median or mode? Player Net Worth ( millions) Michael Jordan 1200 Magic Johnson 600 Shaquille O'Neal 400 Kobe Bryant 350 LeBron James 340 David Robinson 200 Hakeem Olajuwon Kevin Garnett 190 Grant Hill 180 Gary Payton 130 Tim Duncan Dirk Nowitzki 120 Kevin Durant Yao Ming Dwight Howard 100 Find the mean,median and mode Mean – add the numbers and divide by 15: Mean = 292 million Median – find the number in the middle: Median = 190 million Mode – find the number that occurs most: Mode = 120 million Which describes the data better – mean, median or mode? The Median is a better measure – Michael Jordan’s net worth is an outlier that skews the mean too high

You have each team's score from each of its games: There are three different basketball teams and each has played five games. You have each team's score from each of its games: Game 1 Game 2 Game 3 Game 4 Game 5 Jaguars 67 87 54 99 78 Wolves 85 90 44 80 46 Lions 32 101 65 88 55 You want to join one of the basketball teams. You want to join the one that is doing the best so far. Which team would you join?

Scores Mean Median Mode Jaguars 67 87 54 99 78 77 78 none 54 67 78 87 99 Wolves 85 90 44 80 46 none 69 80 44 46 80 85 90 Lions 32 101 65 88 55 68.2 65 none 32 55 65 88 101

Movies that have won the most Oscars Amadeus 8 Ben Hur 11 Best Years of Our Lives 7 Bridge on the River Kwai Caberet Dances with Wolves From Here to Eternity Gigi 9 Going My way Gone with the Wind Lawrence of Arabia Lord of the Rings: Return of the King My Fair Lady 8 On the Waterfront Our of Africa 7 Patton Schindler's List Shakespeare in Love Slumdog Millionaire The English Patient 9 The Last Emporer The Sting Titanic 11 West Side Story 10 Find the mean, median, and mode

Mean Add the numbers and divide by the number of elements Mean = 8.2 Median 8 11 7 9 8 7 9 11 10 The middle number when the numbers are placed in order 7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,9,9,9,10,11,11,11 Median= 8 Mode The number that appears the most Mode= 7 Range The difference between the greatest and smallest number Range = 4