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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.

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

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

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

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

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5. My age. 27 or 29

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

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

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

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

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

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11. The most popular name in the world is?

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

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

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

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15. What travels faster, light or sound?

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

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

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

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

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

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

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

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

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

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

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5. My age. 27 or 29 29

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

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

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

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

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

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

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

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

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

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15. What travels faster, light or sound? Light

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

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

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

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

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

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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

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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

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

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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.

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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

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

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

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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 -0.957 17.976 7.316

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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

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