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Weeks 1&2: Looking at Data  Distributions
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Introduction
Individuals: objects described by a set of data (people, animals, or
things)
Variable: characteristic of an individual. It can take on different values
for different individuals. (Examples: Age, Height, Gender, Favorite
Class, Speed, Moisture, etc.)
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Variables
Dataset
After performing an experiment, survey or conducting a poll we have some
information called a
dataset
.
Example 1
: We asked several students what grade they earned in their
math class and recorded their responses: A, C, D, A, A, B, C, C, B, A
Example 2
: We measured the speed of cars at certain point of the
highway: 66, 71, 25, 50, 45, 55, 69, 77, 80, 47, 100, 70
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Variables
Samples
In statistical language the datasets are called
samples
.
Sample size,
n
,
is the number of elements in a sample. Elements in a sample
correspond to the values of a single variable.
In Examples 1 and 2 the variables are the grade and the speed of the
car. Sample sizes:
n
1
=
10
,
n
2
=
12
There are two main types of variables depending on what kind of values
they take.
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Variables
Type of Variables
Quantitative: numeric values. They can be added, subtracted,
averaged, etc.
Discrete Variable  takes on values which are spaced. That is, for
two adjacent values, there is no value that goes between them.
Continuous Variable  values are all numbers in a given interval.
That is, for two values of a continuous variable that are adjacent,
there is another value that can go between the two.
Categorical: an individual is placed into one of several groups or
categories. These groups or categories are not usually numeric,
although they may appear to be, and numeric functions don’t make
sense. We will discuss these variables in Week 10.
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Variables
Example
Numeric
Variable
Discrete
Continuous
Categorical
Length
O
Hours Enrolled
O
Major
O
Color of Eyes
O
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Variables
Distribution of Variables
Every variable (quantitative or categorical) has a
distribution
of its
values.
The
distribution
of a variable tells us all possible values for the variable
and how often that the variable takes these values.
The distribution has three characteristics:
shape, center and spread
There are two ways to describe a distribution:
with numbers 
statistics
with pictures 
graphs
The type of statistic or graph used depends on the type of variable.
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Variables
Distribution of a Quantitive Variable
Numeric example: the data below shows how much 50 consecutive shoppers
spent in a particular store.
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This note was uploaded on 12/11/2011 for the course STAT 301 taught by Professor Staff during the Spring '08 term at Texas A&M.
 Spring '08
 Staff

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