Statistics 227
Notes
Ch. 1  Basics
Online Notes
o
Individuals: objects described by a set of data
o
Variable: any characteristic of an individual
o
Ask questions when exploring data:
Who are the individuals?
What and how many variables are there?
What purpose does the data have?
o
Categorical variable: places an individual into 1+ groups or categories
o
Quantitative variable: takes numerical values for which arithmetic operations
make sense; usually recorded in a unit of measurement
o
Exploratory data analysis: use of graphs and numerical summaries to
describe the variables in a data set and the relations among them
o
EXPLORING DATA
1. Begin by examining each variable by itself. Then move on to study the
relationships among the variables.
2. Begin with a graph or graphs. Then add numerical summaries of
specific aspects of the data.
o
DISTRIBUTION OF A VARIABLE
Distribution of a variable tells us what values it takes and how often it
takes these values.
Distribution of a categorical variable lists the categories and gives either
the count or the percent of individuals who fall in each category.
o
EXAMINING A HISTOGRAM
In any graph of data, look for the overall pattern and for striking
deviations from that pattern.
You can describe the overall pattern of a histogram by its shape, center,
and spread.
An important kind of deviation is an outlier, an individual value that falls
outside the overall pattern.
o
SYMMETRIC AND SKEWED DISTRIBUTIONS
A distribution is symmetric if the right and left sides of the histogram are
approximately mirror images of each other.
A distribution is skewed to the right if the right side of the histogram
(containing the half of the observations with larger values) extends much
farther out than the left side.
It is skewed to the left if the left side of the histogram extends much
farther out than the right side.
o
Other methods of displaying data:
1) stem plots
2) time plots : plots each observation against the time at which it was
measured
1
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View Full DocumentStatistics 227
Notes
Class Notes – 8/29/07
o
Descriptive statistics
: extract or recapitulate the info content; kernel of
important info is available at a glance
o
Inferential statistics
: produce valid conclusions
o
Unemployment rate
: % of labor force who are not employed for pay
o
Labor force
: all those over 16 who’re either employed, actively seeking work, or
awaiting recall from layoff
o
Condensed array (sort)
: It is an arrangement of the data from lowest to
highest.
Frequency distribution : It is a condensed array or sort of the data.
1) class intervals (bins)
2) count up the observations in the bins
Bins
Frequency
3.0 – 3.9
4
4.0 – 4.9
3
5.0 – 5.9
11
6.0 – 6.9
3
7.0 – 7.9
7
8.0 – 8.9
1
9.0 – 9.9
2
o
Distribution: includes uniform (looks like a rectangle)
Ch. 2  Distributions
Online Notes
o
Mean
: ordinary arithmetic average (x bar)
To find the mean:
Compact notation:
o
Median
: midpoint of a distribution (M)
To find the median of a distribution:
1. Arrange all observations in order of size, from smallest to largest.
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 Fall '08
 Chizmar
 Economics, Least Squares, Standard Deviation

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