3.4 measures of position objectives: by the end of this section, i will be able to… 1) find...
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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.
13. Oregon Coach Bill Bowerman and Phil
Knight bought the Nike swoosh logo from a
student for how much money?
$35 or $65
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.
10. The only Salesianum sport that has not won a state championship.
Basketball or wrestling.
Basketball
13. Oregon Coach Bill Bowerman and Phil
Knight bought the Nike swoosh logo from a
student for how much money? $35 or $65
$35
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
19. The first country music artist to sell over 10
million copies. Garth Brooks or Tim
McGraw.
Garth Brooks
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
+ 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
unusual.• If you are <-3 or >3 it is very unusual
and it is an OUTLIER