Download Measurement II: Quantifying and Describing Variables.

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Sections meet in Sequoyah Hall 142 this week, hold off on
downloading SPSS
Midterm study guide now posted
Office hours 11-1pm today
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You can think of any variable as a
question:
 What is the average lifespan in a country?
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The potential values that the variable can
take on are possible answers to that
question:
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45.9 years (Afghanistan)
71.1 years (The Bahamas)
50.2 years (Benin)
80.7 years (Japan)
IV #1 Wealth. Per
capita GDP takes on
different values in
different countries.
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Haiti $586
Cuba $3267
Spain $18,356
USA $39,678
IV #2 Health. Some
countries have
universal health care,
some don’t.
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Haiti, No
Cuba, Yes
Spain, Yes
USA, No
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Four Levels of Precision
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Measures of Central Tendency
 Mode
 Median
 Mean
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Measures of Dispersion
 Variance, Standard Deviation
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Nominal Measure: You can put cases
into a category, but cannot specify an
order or relationship between the
categories.
 Example: The variable “religion” can take on
values such as Catholic, Protestant, Mormon,
Jewish, etc.

Ordinal Measure: You can put cases into
different categories, and order the
categories.
 Example: The variable “strength of religious
belief” can take on values such as devoutly
religious, fairly religious, slightly religious, not
religious.
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Interval Measure: Not only can you order
the categories of the variable, you can
specify the difference between any two
categories.
 Example. The variable “temperature on the
Fahrenheit scale” can take on values such as
32 degrees, 74 degrees, 116 degrees.

Ratio Measure: You can order categories,
specify the difference between two
categories, and the value of zero on the
variable represents the absence of the
variable.
 Example. The variable “annual income” can
take on the values of $0, $98,000, or
$694,294,129.
Kobe Bryant
Pau Gasol
Steve Nash
Steve Blake
Jordan Hill
Chris Kaman
Jodie Meeks
$30,453,805
$19,285,850
$9,300,500
$4,000,000
$3,563,600
$3,183,000
$1,550,000
Nick Young
Jordan Farmar
Shawne Williams
Wesley Johnson
Xavier Henry
Robert Sacre
Kendall Marshall
Ryan Kelly
$1,106,942
$1,106,942
$1,106,942
$916,099
$916,099
$788,872
$547,570
$490,180
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Mode: The most frequently occurring value.
 $1,106,942
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Median: The midpoint of the distribution of
cases.
 1. Arrange cases in order
 2. If the number of cases is odd, median is the value
taken on by the case in the center of the list.
 3. If the number of cases is even, median is the
average of the two center values. $1,106,942
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Mean is the arithmetic average of the
values that all the cases take on.
$5,221,093
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Add up all the values
 Divide this sum by the number of cases, N.
X 1  X 2  ...  XN  Xi
Mean  X 

N
N
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The variance is a measure of how spread
out cases are, calculated by:
 Compute the distance from each case to
the mean, then square that distance.
 Find the sum of these squared distances,
then divide it by N-1. ~$73 trillion.
(X  X )

Variance 
i
N 1
2
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The standard deviation is the square
root of the variance, $8,555,409.
s  ˆ 
(X  X )
i
N 1
2