103
80
up to
90
2
90
up to
100
7
100
up to
110
6
110
up to
120
9
120
up to
130
8
130
up to
140
7
140
up to
150
3
150
up to
160
3
TOTAL
45
Number of Spots Purchased
Frequency
Frequency Distribution Example
102

Stem-and-leaf Plot Example
103
88
89
96
93
95
96
94
94 97
108
107
103
104
106
103
Stem-and-leaf: Another Example
(Minitab)
104

z
The standard deviation is the most widely used
measure of dispersion.
z
Alternative ways of describing spread of data include
determining the
location
of values that divide a set of
observations into equal parts.
z
These measures include
quartiles, deciles,
and
percentiles.
Quartiles, Deciles and Percentiles
107
LYING
with
Statistics
Often Just Misstatement /
Misunderstanding of Terminology:
z
92% on Test = “In Top 10% of Class”
–
INSTEAD = “Top 10% of Possible Points”
z
92
nd
Percentile = “Twice as High as 46
th”
–
INSTEAD = “92
nd
Percentile scored better
than twice as many people as the 46
th
”

Visualizing Quartiles / Percentiles
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1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
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1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
z
To formalize the computational procedure, let
L
p
refer to the
location of a desired percentile. So if we wanted to find the 33rd
percentile we would use
L
33
and if we wanted the median, the
50th percentile, then
L
50
.
z
The number of observations is
n,
so if we want to locate the
median, its position is at (
n +
1)/2, or we could write this as
(
n +
1)(
P
/100), where
P
is the desired percentile.
Percentile Computation
108

Percentiles - Example
Listed below are the commissions earned last
month by a sample of 15 brokers at Salomon
Smith Barney’s Oakland, California, office.
$2,038 $1,758 $1,721 $1,637
$2,097 $2,047 $2,205 $1,787
$2,287 $1,940 $2,311 $2,054
$2,406 $1,471 $1,460
Locate the median, the first quartile, and the third
quartile for the commissions earned.
108
Percentiles – Example (cont.)
Step 1: Organize the data from lowest to largest
value
$1,460
$1,471
$1,637
$1,721
$1,758
$1,787
$1,940
$2,038
$2,047
$2,054
$2,097
$2,205
$2,287
$2,311
$2,406
108

Percentiles – Example (cont.)
Step 2: Compute the first and third quartiles.
Locate L
25
and L
75
using:
205
,
2
$
721
,
1
$
12
100
75
)
1
15
(
4
100
25
)
1
15
(
75
25
75
25
.
.
L
L
L
L
ly
respective
positions,
12th
and
4th
the
at
located
are
quartiles
third
and
first
the
Therefore,
108
Box Plot - Data Needed
111
A Box Plot needs 5 pieces of data:
z
Minimum Value - Lower Tail
z
Q1 (25th Percentile) - Lower Box
z
Median (Q2 or P50) - Middle of Box
z
Q3 (75th Percentile) - Upper Box
z
Maximum Value - Upper Tail

Box Plot - Example
111
Box Plot Example
Step1: Create an appropriate scale along the horizontal axis.
Step 2: Draw a box that starts at
Q1 (15 minutes) and ends at Q3 (22
minutes). Inside the box we place a vertical line to represent the median (18
minutes).
Step 3: Extend horizontal lines from the box out to the minimum value (13
minutes) and the maximum value (30 minutes).
111

Box Plot – Using Minitab
Develop a box plot of the data for the data below from Chapter 2. What can we
conclude about the distribution of the vehicle selling prices?

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- Spring '11
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- Standard Deviation