3 4 measures of position
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3.4 Measures of Position. Objectives: By the end of this section, I will be able to… Find percentiles for both small and large data sets. Calculate z -scores, and explain why we use them. Use z -scores to detect outliers.

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3.4 Measures of Position

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3.4 Measures of Position

Objectives:

By the end of this section, I will be

able to…

  • Find percentiles for both small and large data sets.

  • Calculate z-scores, and explain why we use them.

  • Use z-scores to detect outliers.


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 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

  • Two ways to compare scores:

    • Percentile Rank

    • Z-scores


PERCENTILE RANK

# of Equal scores

Scores that came BEFORE

  • 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

Total Number


PERCENTILE RANK

# of Equal scores

Scores that came BEFORE

  • Find your percentile rank.

Total Number


z-scores

  • Numerical values that are used to compare scores

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


z-scores

MEAN

1) Find your z-score.

  • Let’s find the meanfirst.

  • Now find the standard deviation.

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


Finding an actual score

  • 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 -0.957

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


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