P1259088317ZMgua

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STATISTICS
ELEMENTARY
Section 2-6 Measures of Position
MARIO F. TRIOLA
EIGHTH
EDITION
2
Measures of Position

• z Score (or standard score)
• the number of standard deviations that a
  given value x is above or below the mean

3
Measures of Position z score

• Sample

Population
x - µ
x - x
z
z
?
s
Round to 2 decimal places
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FIGURE 2-16
Interpreting Z Scores
Unusual Values
Unusual Values
Ordinary Values
- 3
- 2
- 1
0
1
2
3
Z
5
Measures of Position
Quartiles, Deciles, Percentiles
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Quartiles
Q1, Q2, Q3 divides ranked scores into four
equal parts
25
25
25
25
Q3
Q2
Q1
(minimum)
(maximum)
(median)
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Deciles
D1, D2, D3, D4, D5, D6, D7, D8, D9 divides ranked
data into ten equal parts
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Percentiles

• 99 Percentiles
• They divide the data into 100 parts.
• Example A score is the 35th percentile if 35 of
  the scores are below it.
• Data must be arranged lowest to highest before
  finding percentiles.

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Finding Percentile of a Given Score
number of scores less than x
Percentile of score x
100
total number of scores
Find percentile rank of 0.8152.
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11/36?100 30.55556
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Round to 31
The percentile rank of 0.8152 is 31.
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Finding Score Given a Percentile
n total number of values in the data set k
percentile being used L locator that gives the
position of a value Pk kth percentile
The goal is to have k of the scores below Pk.
If L is a whole number, add 1 to it. If L is
not a whole number, round it UP to the next whole
number. Then starting from the lowest score,
find the Lth score in the list. That will be Pk.
11
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Find P31 (the 31st percentile).
Round UP to 12.
Starting with the smallest, count up to the 12th
item in the list.
P31 is 0.8152.
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Quartiles

• Q1 P25
• Q2 P50
• Q3 P75