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 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
• 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-scores
1) Find your z-score.
• Let’s find the mean first.
• Now find the standard deviation.
x xz
s
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 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 5.1Betty Sue who had a z-score of -0.957
x xz
s
95.1
1.76
x
90.957
1.76
x 17.97
67.316
z-scores and OUTLIERS• If you are between -2 and 2 it is NOT