M ARIO F . T RIOLA
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Transcript of M ARIO F . T RIOLA
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1Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
MARIO F. TRIOLA EIGHTH
EDITION
ELEMENTARY STATISTICSSection 2-6 Measures of Position
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2Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Measures of Position
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3Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
z Score (or standard score)the number of standard deviations that a given value x is above or
below the mean
Measures of Position
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4Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Sample
z = x - xs
Measures of Positionz score
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5Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Sample
z = x - xs
Population
z = x - µ
Measures of Positionz score
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6Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Sample
z = x - xs
Population
z = x - µ
Round to 2 decimal places
Measures of Positionz score
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7Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
- 3 - 2 - 1 0 1 2 3
Z
Unusual Values
Unusual Values
OrdinaryValues
Interpreting Z ScoresFIGURE 2-16
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8Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Measures of Position
Quartiles, Deciles,Percentiles
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9Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Quartiles
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10Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Q1, Q2, Q3
Quartiles
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11Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Q1, Q2, Q3
divides ranked scores into four equal parts
Quartiles
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12Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Q1, Q2, Q3 divides ranked scores into four equal parts
Quartiles
25% 25% 25% 25%
Q3Q2Q1
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13Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Q1, Q2, Q3 divides ranked scores into four equal parts
Quartiles
25% 25% 25% 25%
Q3Q2Q1(minimum) (maximum)
(median)
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14Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
D1, D2, D3, D4, D5, D6, D7, D8, D9
divides ranked data into ten equal parts
Deciles
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15Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
D1, D2, D3, D4, D5, D6, D7, D8, D9
divides ranked data into ten equal parts
Deciles
10% 10% 10% 10% 10% 10% 10% 10% 10% 10%
D1 D2 D3 D4 D5 D6 D7 D8 D9
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16Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
99 Percentiles
Percentiles
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17Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Quartiles, Deciles, Percentiles
Fractiles
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18Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Quartiles, Deciles, Percentiles
Fractiles(Quantiles)
partitions data into approximately equal parts
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19Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Finding the Percentile of a Given Score
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20Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Finding the Percentile of a Given Score
Percentile of score x = • 100number of scores less than x
total number of scores
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21Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Finding the Score Given a Percentile
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22Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Finding the 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
L = • nk100
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23Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Finding the Value of the
kth Percentile
Sort the data.(Arrange the data in order of lowest to highest.)
The value of the kth percentileis midway between the Lth valueand the next value in thesorted set of data. Find Pk byadding the L th value and thenext value and dividing the total by 2.
Start
ComputeL = n where
n = number of valuesk = percentile in question
)( k100
Change L by rounding it up to the nextlarger whole number.
The value of Pk is theLth value, counting from the lowest
Is L a whole
number?
Yes
No
Figure 2-17
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24Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
QuartilesQ1 = P25
Q2 = P50
Q3 = P75
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25Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
QuartilesQ1 = P25
Q2 = P50
Q3 = P75
D1 = P10 D2 = P20
D3 = P30
• • •D9 = P90
Deciles
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26Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Interquartile Range (or IQR): Q3 - Q1
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27Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Interquartile Range (or IQR): Q3 - Q1
Semi-interquartile Range:2
Q3 - Q1
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28Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Interquartile Range (or IQR): Q3 - Q1
Semi-interquartile Range:
Midquartile: 2
2
Q3 - Q1
Q1 + Q3
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29Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Interquartile Range (or IQR): Q3 - Q1
Semi-interquartile Range:
Midquartile:
10 - 90 Percentile Range: P90 - P10
2
2
Q3 - Q1
Q1 + Q3
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30Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Assignment
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