Basic concepts
The population is the entire collection of individuals or measurements
about which information is desired. A sample is a subset of the
population that is selected for study. A statistic is a numerical
characteristic of the sample, from which inferences about the population's parameters
-- numerical characteristics of the population -- can be drawn.
Types of statistics
 | Numerical, graphical, and tabular methods for organizing and summarizing
data |
| Methods of generalizing from a sample to the population from which the
sample was selected |
The goal of inferential statistics is to use sample statistics to make
inference about population parameters.
|
 | Categorical
and Numerical Variables
|
 | Any characteristic which varies or changes when moving from
individual to individual or object to object in a population.
| (Qualitative) Variable A variable whose values cannot be
interpreted as numbers.
| (Quantitative) Variable Measurements or counts, values which have
meanings as numbers.
| set A collection of observations on one or more variables. |
| | |
| Continuous
and Discrete Data
|
Data consisting of numerical (quantitative) variables can be further
divided into two groups: discrete and continuous.
- If the set of all possible values, when pictured on the number
line, consists only of isolated points.
- If the set of all values, when pictured on the number line,
consists of intervals.
The most common type of discrete variable we will encounter is a counting
variable.
| Univariate,
Bivariate, and Multivariate Data
|
Depending on how many variables we are measuring on the individuals
or objects in our sample, we will have one of the three following types
of data sets:
| Measurements made on only one variable per observation.
| Measurements made on two variables per observation.
| Measurements made on many variables per observation. |
| |
In this course, we will concentrate on univariate and bivariate data
sets.
| The
Concept of ``Distribution''
|
Measurements on any variable, even the same variable on the same
subject, will always vary. The pattern of variation of a variable is
called its distribution, which can be described both
mathematically and graphically. In essence, the distribution records all
possible numerical values of a variable and how often each value occurs
(its frequency). The most famous example of a distribution is the
bell-shaped curve. To see examples of several types of distributions,
see the ``How are things distributed'' concept lab.
|
| | | | | | |
|
| Describing
One Sample or Population
| Graphically
|
Statistics begins with skills and principles for examining data. In
this section, we will learn how to graphically display univariate data.
The following principles apply:
| To interpret data, you must first know their context, i.e., their
origin, manner of collection, etc.
| Always examine the data. Specifically look for
- Regular overall pattern in data.
- Important deviations from that pattern.
|
|
NOTE: Observations which do not
follow the regular pattern (sometimes called outliers) should
not be removed from the data unless there is good reason to do so. A
``good'' reason could be that the outlier is a ``typo'' or that the
equipment used to measure the observation failed. In other words, the
removal of extreme observations should be based on technical or
scientific knowledge rather than mere habit. Sometimes, in fact, we are
interested in finding outliers. For instance, universities like to give
scholarships to students who have unusually high scores on standardized
tests such as the ACT or SAT.
| Numerical
Descriptive Statistics
|
Histograms provide a good graphical means for visualizing sample
(population) distributions and for comparing more than one sample
(population). Numerical summary statistics provide additional
information for describing and comparing samples (populations). We will
be concerned primarily with two types of numerical summary statistics,
- Measures of Location
| Measures of Center
| Other Measures |
|
Measures of Variability
|
| | |
|
Internet References
Related pages in this website
Geometry Glossary
Number Theory Glossary
Topology Glossary
|
