(Continue) Chapter 1: Examining Distributions
1.2 Describing Distributions with numbers:
Center and Spread:
To get a useful numerical description of a distribution, we need to have both some
measure of center and some measure of spread.
Measuring center:
Provide some notion of what value the distribution is grouped around.
The most common measures are the mean and median.
The Mean
x
: also called the arithmetic average, represent the balance point for
quantitative data.
x
=
x
1
+
x
2
+
...
+
x
n
n
=
x
i
i
=
1
n
∑
n
This is the sum of the observations divided by the sample size.
Example: This data set is the first 11 games of the men’s basketball team.
DATE
OPPONENT
W/L
SCORE
ATTEND





11/16/09
JACKSONVILLE
W
8761
6493
11/18/09
STETSON
W
8038
6525
11/21/09
at Mercer
W
8950
3200
11/24/09
at Florida
L
5268
11239
11/26/09
vs Iona
W
5449
2149
11/27/09
vs Alabama
W
6051
1915
11/29/09
vs Marquette
W
5756
2225
12/2/09
at Ohio State
L
6477
13514
12/6/09
FIU
W
8262
5168
12/15/09
GEORGIA STATE
W
6255
5281
12/17/09
AUBURN
W
7672
6063
Example: Find the mean score of the first 11 games that FSU played in Fall 09.
x
=
87
+
80
+
89
+
52
+
54
+
60
+
57
+
64
+
82
+
62
+
76
11
=
763
11
=
69.3636
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View Full DocumentMedian:
is the middle value
this value and 50% lie abov
Steps:
1.
Arrange the data valu
2.
If the number of data
observation on the o
(n+1)/2 observation
3.
If the number of data
center observations
(n+1)/2 from the bo
*Note that the formula (n+1
median in the ordered list.
Odd data set Example
: fin
Home games=(6493, 6
x
=
M=
Even data setExample
: fin
from home games.
Away games= (3200, 11239
x
=
M=
Mean vs. Median
•
The mean is GREATLY affected
•
The median is NOT affected by
•
If the mean and median are (a
symmetric.
•
If mean<median, distribution
•
If mean> median, distribution
•
*NOTE: when it is skewed the
e of an ordered data set. (i.e. 50% of the value
ve this value).
es in an ascending order (from smallest to lar
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 Spring '08
 BATEH
 Statistics, Standard Deviation, Interquartile range

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