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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
2Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Measures of Position
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
4Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Sample
z = x - xs
Measures of Positionz score
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
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
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
8Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Measures of Position
Quartiles, Deciles,Percentiles
9Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Quartiles
10Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Q1, Q2, Q3
Quartiles
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
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
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)
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
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
16Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
99 Percentiles
Percentiles
17Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Quartiles, Deciles, Percentiles
Fractiles
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
19Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Finding the Percentile of a Given Score
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
21Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Finding the Score Given a Percentile
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
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
24Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
QuartilesQ1 = P25
Q2 = P50
Q3 = P75
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
26Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Interquartile Range (or IQR): Q3 - Q1
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
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
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
30Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Assignment
• Page 99:• 1- 35 odds
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