![Page 1: 1 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION E LEMENTARY](https://reader036.vdocuments.net/reader036/viewer/2022081603/56649f2b5503460f94c45bbe/html5/thumbnails/1.jpg)
1Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
MARIO F. TRIOLAMARIO F. TRIOLA EIGHTHEIGHTH
EDITIONEDITION
ELEMENTARY STATISTICSSection 2-6 Measures of Position
![Page 2: 1 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION E LEMENTARY](https://reader036.vdocuments.net/reader036/viewer/2022081603/56649f2b5503460f94c45bbe/html5/thumbnails/2.jpg)
2Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Measures of Position
![Page 3: 1 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION E LEMENTARY](https://reader036.vdocuments.net/reader036/viewer/2022081603/56649f2b5503460f94c45bbe/html5/thumbnails/3.jpg)
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
![Page 4: 1 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION E LEMENTARY](https://reader036.vdocuments.net/reader036/viewer/2022081603/56649f2b5503460f94c45bbe/html5/thumbnails/4.jpg)
4Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Sample
z = x - xs
Measures of Positionz score
![Page 5: 1 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION E LEMENTARY](https://reader036.vdocuments.net/reader036/viewer/2022081603/56649f2b5503460f94c45bbe/html5/thumbnails/5.jpg)
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
![Page 6: 1 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION E LEMENTARY](https://reader036.vdocuments.net/reader036/viewer/2022081603/56649f2b5503460f94c45bbe/html5/thumbnails/6.jpg)
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
![Page 7: 1 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION E LEMENTARY](https://reader036.vdocuments.net/reader036/viewer/2022081603/56649f2b5503460f94c45bbe/html5/thumbnails/7.jpg)
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 Scores
FIGURE 2-16
![Page 8: 1 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION E LEMENTARY](https://reader036.vdocuments.net/reader036/viewer/2022081603/56649f2b5503460f94c45bbe/html5/thumbnails/8.jpg)
8Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Measures of Position
Quartiles, Deciles,
Percentiles
![Page 9: 1 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION E LEMENTARY](https://reader036.vdocuments.net/reader036/viewer/2022081603/56649f2b5503460f94c45bbe/html5/thumbnails/9.jpg)
9Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Quartiles
![Page 10: 1 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION E LEMENTARY](https://reader036.vdocuments.net/reader036/viewer/2022081603/56649f2b5503460f94c45bbe/html5/thumbnails/10.jpg)
10Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Q1, Q2, Q3
Quartiles
![Page 11: 1 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION E LEMENTARY](https://reader036.vdocuments.net/reader036/viewer/2022081603/56649f2b5503460f94c45bbe/html5/thumbnails/11.jpg)
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
![Page 12: 1 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION E LEMENTARY](https://reader036.vdocuments.net/reader036/viewer/2022081603/56649f2b5503460f94c45bbe/html5/thumbnails/12.jpg)
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
![Page 13: 1 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION E LEMENTARY](https://reader036.vdocuments.net/reader036/viewer/2022081603/56649f2b5503460f94c45bbe/html5/thumbnails/13.jpg)
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)
![Page 14: 1 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION E LEMENTARY](https://reader036.vdocuments.net/reader036/viewer/2022081603/56649f2b5503460f94c45bbe/html5/thumbnails/14.jpg)
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
![Page 15: 1 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION E LEMENTARY](https://reader036.vdocuments.net/reader036/viewer/2022081603/56649f2b5503460f94c45bbe/html5/thumbnails/15.jpg)
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
![Page 16: 1 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION E LEMENTARY](https://reader036.vdocuments.net/reader036/viewer/2022081603/56649f2b5503460f94c45bbe/html5/thumbnails/16.jpg)
16Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
99 Percentiles
Percentiles
![Page 17: 1 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION E LEMENTARY](https://reader036.vdocuments.net/reader036/viewer/2022081603/56649f2b5503460f94c45bbe/html5/thumbnails/17.jpg)
17Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Quartiles, Deciles, Percentiles
Fractiles
![Page 18: 1 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION E LEMENTARY](https://reader036.vdocuments.net/reader036/viewer/2022081603/56649f2b5503460f94c45bbe/html5/thumbnails/18.jpg)
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
![Page 19: 1 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION E LEMENTARY](https://reader036.vdocuments.net/reader036/viewer/2022081603/56649f2b5503460f94c45bbe/html5/thumbnails/19.jpg)
19Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Finding the Percentile of a Given Score
![Page 20: 1 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION E LEMENTARY](https://reader036.vdocuments.net/reader036/viewer/2022081603/56649f2b5503460f94c45bbe/html5/thumbnails/20.jpg)
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
![Page 21: 1 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION E LEMENTARY](https://reader036.vdocuments.net/reader036/viewer/2022081603/56649f2b5503460f94c45bbe/html5/thumbnails/21.jpg)
21Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Finding the Score Given a Percentile
![Page 22: 1 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION E LEMENTARY](https://reader036.vdocuments.net/reader036/viewer/2022081603/56649f2b5503460f94c45bbe/html5/thumbnails/22.jpg)
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
![Page 23: 1 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION E LEMENTARY](https://reader036.vdocuments.net/reader036/viewer/2022081603/56649f2b5503460f94c45bbe/html5/thumbnails/23.jpg)
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 percentile
is midway between the Lth value
and the next value in the
sorted set of data. Find Pk by
adding the L th value and the
next value and dividing the
total by 2.
Start
Compute
L = n where
n = number of values
k = percentile in question
)( k100
Change L by rounding
it up to the next
larger whole number.
The value of Pk is the
Lth value, counting from the lowest
Is L a whole
number?
Yes
No
Figure 2-17
![Page 24: 1 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION E LEMENTARY](https://reader036.vdocuments.net/reader036/viewer/2022081603/56649f2b5503460f94c45bbe/html5/thumbnails/24.jpg)
24Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Quartiles
Q1 = P25
Q2 = P50
Q3 = P75
![Page 25: 1 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION E LEMENTARY](https://reader036.vdocuments.net/reader036/viewer/2022081603/56649f2b5503460f94c45bbe/html5/thumbnails/25.jpg)
25Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Quartiles
Q1 = P25
Q2 = P50
Q3 = P75
D1 = P10
D2 = P20
D3 = P30
• • •
D9 = P90
Deciles
![Page 26: 1 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION E LEMENTARY](https://reader036.vdocuments.net/reader036/viewer/2022081603/56649f2b5503460f94c45bbe/html5/thumbnails/26.jpg)
26Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Interquartile Range (or IQR): Q3 - Q1
![Page 27: 1 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION E LEMENTARY](https://reader036.vdocuments.net/reader036/viewer/2022081603/56649f2b5503460f94c45bbe/html5/thumbnails/27.jpg)
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
![Page 28: 1 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION E LEMENTARY](https://reader036.vdocuments.net/reader036/viewer/2022081603/56649f2b5503460f94c45bbe/html5/thumbnails/28.jpg)
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
![Page 29: 1 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION E LEMENTARY](https://reader036.vdocuments.net/reader036/viewer/2022081603/56649f2b5503460f94c45bbe/html5/thumbnails/29.jpg)
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