1
STAT 2000
Sections 2.52.6
Measures of Position
Statistics: The Art and Science of Learning
from Data
AgrestiFranklin
Measures of Position
Percentiles
The pth percentile is the value below which you
have p% of the data.
Example
: If a value lies at the 30
th
percentile, then
approximately 30% of the values are less than this
value, and approximately 70% of the values are
greater than this value.
Notation
: P
30
is the 30
th
percentile.
If John graduated at the 78th percentile in a
class of 876, approximately how many students
ranked below John?
Joan learned that she would graduate ranked
47th (from the top) in a class of 876.
Joan
graduated at the _____ percentile of her class.
Measures of Position:
Quartiles
Quartiles divide the data into 4 equal parts.
25%

25%

25%

25%
Q1
Q2
Q3
Q1: First Quartile is the 25
th
percentile.
(25% below and 75% above)
Q2: Second Quartile is the 50
th
percentile.
(50% below and 50% above)
Q2 is also the median.
Q3: Third Quartile is the 75
th
percentile.
(75% below and 25% above)
25%

25%

25%

25%
Q1
Q2
Q3
P
25
P
50
P
75
median
D t
Finding Quartiles
First find the median.
Then find the middle value
of the upper and lower halves.
Remember the data must be in order!
Data:
20
19
30
18
17
22
Data
20
19
30
18
17
22
23
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