3.4 Measures of PositionObjectives:By the end of this section, I will beable 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 Lord’s 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?

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 Lord’s Prayer

appear in the Bible? 1 or 2

2

7. What year was Salesianum started?

1903 or 1906.

1903

8. “Jingle Bells” was actually written for

which holiday? Halloween or Thanksgiving

Thanksgiving

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

or 21

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

•Two ways to compare scores:–Percentile Rank–Z-scores

PERCENTILE RANK

• B = # of scores that came BEFORE “your” score

• E = # of scores that are the same as “your” score

• N = Total # of people taking the test

12 100

B EP

N

# of Equal scores

Total Number

Scores that came BEFORE

PERCENTILE RANK

1)Find your percentile rank.

12 100

B EP

N

# of Equal scores

Total Number

Scores that came BEFORE

z-scores•Numerical values that are used to compare scores

• It indicates how many standard deviations a data value is from the mean.

z-scores1) Find your z-score.

• Let’s find the mean first.

• Now find the standard deviation.

x xzs

MEAN

Standard

Deviation

USE DECIMALS FOR z-scores.

• 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

x

x

x

Finding an actual score2) 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 5.1Betty Sue who had a z-score of -0.957

x xzs

95.11.76x

90.957

1.76x

17.976 7.316

z-scores and OUTLIERS• If you are between -2 and 2 it is NOT

unusual.• If you are <-3 or >3 it is very unusual

and it is an OUTLIER