# Introduction to Statistics…

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```							Introduction to Statistics

Chapter 1
Introduction to Statistics

Lecture 2       1
Introduction to Statistics… Chapter 1

Overview
A common goal of studies and surveys and other
data collecting tools is to collect data from a small
part of a larger group so we can learn something

In this section we will look at some of the ways to
describe data.

Lecture 2                     2
Introduction to Statistics… Chapter 1

Definitions
Data
Observations (such as measurements, genders,
survey responses) that have been collected
Statistics
a collection of methods for planning studies and
experiments, obtaining data, and then organizing,
summarizing, presenting, analyzing, interpreting, and
drawing conclusions based on the data

Lecture 2                       3
Introduction to Statistics… Chapter 1

Definitions
Population
the complete collection of all elements (scores, people,
measurements, and so on) to be studied; the collection
is complete in the sense that it includes all subjects to
be studied
Census
Collection of data from every member of a population
Sample
Sub collection of members selected from a population
Lecture 2                         4
Introduction to Statistics… Chapter 1

Lecture 2         5
Introduction to Statistics… Chapter 1

Parameter
a numerical measurement describing some
characteristic of a population.

Population

Parameter
Lecture 2            6
Introduction to Statistics… Chapter 1

Statistic
a numerical measurement describing some
characteristic of a sample.

Sample

Statistic
Lecture 2             7
Introduction to Statistics… Chapter 1

Common Summary Measures
Sample Statistic       Population Parameter

Mean              X                        

Standard
Deviation         S                         

Variance          S2                       2

Lecture 2                          8
Introduction to Statistics… Chapter 1

Types of Data
Data

Lecture 2         9
Introduction to Statistics… Chapter 1

Quantitative data
Numbers representing counts or measurements.
Example: The income of college graduates

Qualitative (or attribute) data
can be separated into different categories that are distinguished
by some nonnumeric characteristic
Example: The genders (male/female)

Lecture 2                            10
Introduction to Statistics… Chapter 1

Working with Quantitative Data

Quantitative data can further be described by
distinguishing between discrete and continuous
types.

Lecture 2                 11
Introduction to Statistics… Chapter 1

Discrete data
Result when the number of possible values is
either a finite number or a ‘countable’
number
(i.e. the number of possible values is
0, 1, 2, 3, . .)

Example: The number of Lumps that a
factory can produce
Lecture 2                  12
Introduction to Statistics… Chapter 1

Continuous (numerical) data
Result from infinitely many possible values that
correspond to some continuous scale that covers
a range of values without gaps, interruptions, or
jumps

Lecture 2                  13
Introduction to Statistics… Chapter 1

Uses & Abuses of Statistics

Lecture 2         14
Introduction to Statistics… Chapter 1

Voluntary response sample
(or self-selected sample)

one in which the respondents themselves
decide whether to be included

In this case, valid conclusions can be made only
about the specific group of people who agree to
participate.
Lecture 2                     15
Introduction to Statistics… Chapter 1

Misuse # 2- Small Samples
Conclusions should not be based on samples that
are far too small.
Example: Basing a school suspension rate on a
sample of only three students

Lecture 2                  16
Introduction to Statistics… Chapter 1

Misuse # 3- Graphs

To correctly
interpret a graph,
you must analyze
the numerical
information given
in the graph, so as
not to be misled by
the graph’s shape.

Lecture 2        17
Introduction to Statistics… Chapter 1

Misuse # 4- Pictographs
Part (b) is
designed to
exaggerate
the
difference by
increasing
each
dimension in
proportion to
the actual
amounts of
oil
Lecture 2         18
consumption
Introduction to Statistics… Chapter 1

Misuse # 5- Percentages

sometimes used. For example, if you take
100% of a quantity, you take it all. 110% of
an effort does not make sense.

Lecture 2                  19
Introduction to Statistics… Chapter 1

Sample Size

Lecture 2         20
Introduction to Statistics… Chapter 1

Sample Size
use a sample size that is large enough to see the
true nature of any effects and obtain that sample
using an appropriate method, such as one based
on randomness

Lecture 2                   21
Introduction to Statistics… Chapter 1

Random Sample
Members of the population are selected in
such a way that each individual member has an
equal chance of being selected

Lecture 2                   22
Introduction to Statistics… Chapter 1

Methods of Sampling
Random
Sampling
selection so that
each
individual
member has an
equal chance of
being selected

Lecture 2         23
Introduction to Statistics… Chapter 1

Systematic Sampling
Select some starting point and then
select every k th element in the population

Lecture 2                   24
Introduction to Statistics… Chapter 1

Convenience Sampling
use results that are easy to get

Lecture 2            25
Introduction to Statistics… Chapter 1

Stratified Sampling
subdivide the population into at
least two different subgroups that share the same
characteristics, then draw a sample from each subgroup

Lecture 2                      26
Introduction to Statistics… Chapter 1

Cluster Sampling
divide the population into sections
(or clusters); randomly select some of those clusters; choose all
members from selected clusters

Lecture 2                         27
Introduction to Statistics… Chapter 1

Methods of Sampling - Summary

Random

Systematic

Convenience

Stratified

Cluster

Lecture 2         28

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