3.4 Measures of Position Objectives: By the end of this section, I will be able to… 1) Find percentiles for both small and large data sets. 2) Calculate z-scores, and explain why we use them. 3) Use z-scores to detect outliers.

1.How many different types of animals are in a box of animal crackers? 18 or 7

2. How many total dots are on a pair of dice? 6 or 42

3. The kings in a deck of cards each represent a great king from history. T or F

4. There are no clocks in a Las Vegas gambling casino. T or F

5. My age. 27 or 29

6. How many times does the Lords Prayer appear in the Bible? 1 or 2

7. What year was Salesianum started? 1903 or 1906.

8. Jingle Bells was actually written for which holiday? Halloween or Thanksgiving

9. How many Qs are in a Scrabble game? 1 or 2

10. The only Salesianum sport that has not won a state championship. Basketball or wrestling.

11. The most popular name in the world is?

12. What is the name of the Camel on the back of Camel cigarettes? Old John or Old Joe

13. Oregon Coach Bill Bowerman and Phil Knight bought the Nike swoosh logo from a student for how much money? $35 or $65

14. Tigers have striped fur. What else is striped? Skin or Eyes

15. What travels faster, light or sound?

16. This U.S. state boasts the highest amount of residents who were born in other countries. California or New York.

17. On which vegetable did Egyptians used to place their hand over when under oath? Onion or a Carrot.

18. What is the top selling spice in the world? Pepper or Salt

19. The first country music artist to sell over 10 million copies. Garth Brooks or Tim McGraw.

20. What sport used the term home run before baseball? Lacrosse or Cricket.

HOW MANY DID YOU GET RIGHT? HOW MANY DID YOU GET RIGHT?

1. How many different types of animals are in a box of animal crackers? 18

2. How many total dots are on a pair of dice? 42

3. The kings in a deck of cards each represent a great king from history. T or F T

4. There are no clocks in a Las Vegas gambling casino. T or F T

5. My age. 27 or 29 29

6. How many times does the Lords Prayer appear in the Bible? 1 or 2 2

7. What year was Salesianum started? 1903 or

8. Jingle Bells was actually written for which holiday? Halloween or Thanksgiving Thanksgiving

9. How many Qs are in a Scrabble game? 1 or 2 1

10. The only Salesianum sport that has not won a state championship. Basketball or wrestling. Basketball

11. The most popular name in the world is? Muhammed

12. What is the name of the Camel on the back of Camel cigarettes? Old John or Old Joe Old Joe

13. Oregon Coach Bill Bowerman and Phil Knight bought the Nike swoosh logo from a student for how much money? $35 or $65 $35

14. Tigers have striped fur. What else is striped? Skin or Eyes Skin

15. What travels faster, light or sound? Light

16. This U.S. state boasts the highest amount of residents who were born in other countries. California or New York. Cali

17. On which vegetable did Egyptians used to place their hand over when under oath? Onion or a Carrot. Onion

18. What is the top selling spice in the world? Pepper or Salt Pepper

19. The first country music artist to sell over 10 million copies. Garth Brooks or Tim McGraw. Garth Brooks

20. What sport used the term home run before baseball? Lacrosse or Cricket. Cricket

Comparing Scores Standardized Tests: SATs, TerraNovas, CTBS, ACTs Standardized Tests: SATs, TerraNovas, CTBS, ACTs Two ways to compare scores: Two ways to compare scores: –Percentile Rank –Z-scores

PERCENTILE RANK B = # of scores that came BEFORE your score B = # of scores that came BEFORE your score E = # of scores that are the same as your score E = # of scores that are the same as your score N = Total # of people taking the test N = Total # of people taking the test # of Equal scores Total Number Scores that came BEFORE

PERCENTILE RANK 1) Find your percentile rank. # of Equal scores Total Number Scores that came BEFORE

z-scores Numerical values that are used to compare scores Numerical values that are used to compare scores It indicates how many standard deviations a data value is from the mean. It indicates how many standard deviations a data value is from the mean.

z-scores 1) Find your z-score. Lets find the mean first. Lets find the mean first. Now find the standard deviation. Now find the standard deviation. MEAN Standard Deviation

USE DECIMALS FOR z-scores. We want them to be as accurate as possible! We want them to be as accurate as possible!

+ z-score means you are ABOVE the - z-score means you are BELOW the 0 z-score means you are the exactly

Finding an actual score 2) If the average senior at UD can drink 9 beers before he/she gets sick with a standard deviation of 1.76, find the amount that the following people actually drank. Timmy Joe who had a z-score of 5.1 Betty Sue who had a z-score of

z-scores and OUTLIERS If you are between -2 and 2 it is NOT unusual. If you are between -2 and 2 it is NOT unusual. If you are 3 it is very unusual and it is an OUTLIER If you are 3 it is very unusual and it is an OUTLIER