Mean, Median, Mode

Tuesday 9/18/12Theme, sports

What you will learn (Content purpose)

• Perform common calculations required for data analysis.

Language Purpose (What you will say)

Use the following terms • Mean, • Median• mode.• Range

What you will do with your group (PGW Outcome)

• Calculate mean, median, and mode.

Analyzing Data• We will use the following terms to

understand our data: Mean, median, mode, and range.

Example of Mean• Turn to pg NOS 15 of your text

Mean is used in your grade average

MEAN• The sum of the

numbers in a data set divided by the total entries in a set

• In other words: “Add up all the numbers and then divide by how many there are.”

• Also known as the “AVERAGE”

Finding MeanLet’s find your mean running time for the mile over the course of four days:• Day one: 8 min• Day two: 7 min• Day three: 9 min• Day four: 6 minAdd up all of the times, then divide by 4 days. What do you get?

Examples of Mean Salaries in sports

The national hockey league Major league baseball

• The National Hockey League had an average salary (2007) of $1,906,793

• Major League Baseball's average salary per player (in the 2010 season) was $3,297,828

Median• Is the middle number in a data set when the data

are arranged in numerical order• In other words. . . “Put all the numbers in order,

and then count in find the middle number.”

Finding Median• Michael Phelps wants

to find the Median of his swim times for the 200 meter butterfly today. He swam 13 times and then put the times in order from fastest to slowest.

• What was his median time?

Trial Time for 200 m Fly

1 1 min. 54.53 sec

5 1 min. 60 sec

13 2 min. 02.11 sec

3 2 min. 12.45 sec

12 2 min. 15.03 sec

11 2 min. 25.49 sec

2 2 min. 30 sec

10 2 min. 34.02 sec

9 2 min. 48.23 sec

4 2 min. 59.03 sec

7 2 min. 59.49 sec

8 3 min. 56.38 sec

6 5 min. 38.56 sec

But what if….• (if you have an even

number of data items, add the two middle numbers together and divide by two to find the median)

Mode• Mode is the number or item that appears most

often.• In other words- “It’s the thing you see most in a

list of things. It happens the most.”

What is the mode?

Finding Mode• Cam Newton, the

Quarterback on the Carolina Panthers football team wants to find the Mode for his touchdowns scored during games.

• What number occurs most frequently?

Game Number of Touchdowns

1 0

2 2

3 4

4 0

5 2

6 2

7 1

8 5

9 2

Is Mode the same as Median ?

• How are mode and median different from one another? No.

Mode is the number that occurs the most often, while Median is the number that’s in the middle of a data set.

Is mean the same as mode ?

14 players = >$2 million +2009-10 Tampa Bay Buccaneers Salaries - USATODAY.com

44 players = <$2 million

• The 2009 National Football League season, the mean player salary was $1.1 million.

• This number is severely skewed as there are only a couple of players on a team making a salary of around $7 million to $8 million, while a larger number make toward the league minimum.

• The league minimum for rookies in 2009 was $193,000. This was the mode since most players make this much.

Tampa Bay Buccaneers Salaries

Mean vs Median. . . • As of the 2008

season, Major League Soccer's average/mean salary was $117,299.

• The median salary however was $55,000.

• In 2008, the highest salary was $5.5 million for David Beckham, and the second highest salary went to Cuauhtemoc Blanco at $2,492,316.

Range• The difference between the greatest number and

the least number in the data set.• In other words: “Take the biggest number and

subtract the smallest number.”

Finding Range• Derek Jeter wanted to

find his range of homeruns scored in a game this season.

• What is his range?

Game Number of homeruns

1 2

2 4

3 7

4 9

5 1

6 0

7 5

8 7

9 2

10 3

Mean, Median, Mode, Range

• Please come up with a problem for each on your own paper.