Download OBJECTIVES Variables and Types of Data

M227
Chapter 1
Nature of Probability and Statistics
OBJECTIVES
Demonstrate knowledge of statistical terms.
Differentiate between the two branches of statistics.
Identify types of data.
Identify the measurement level for each variable.
Identify the four basic sampling techniques.
Explain the difference between an observational and an experimental study.
Explain how statistics can be used and misused.
Explain the importance of computers and calculators in statistics.
Statistics is the science of conducting studies to collect, organize, summarize, analyze,
and draw conclusions from data.
Descriptive statistics consists of the collection, organization, summarization, and
presentation of data.
Inferential statistics consists of generalizing from samples to populations, performing
estimations hypothesis testing, determining relationships among variables, and making
predictions. (Probability, Hypothesis testing, relationships between variables, predictions)
Probability is the chance of an event occurring.
A population consists of all subjects that are being studied.
A sample is a group of subjects selected from a population.
Variables and Types of Data
In order to gain knowledge about seemingly haphazard events, statisticians collect
information for variables that describe the events.
A variable is a characteristic or attribute that can assume different values.
Data are the values that variables can assume.
A data set is a collection of data values.
Each value in the data set is called a data value or a datum.
Random variables have values that are determined by chance.
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M227
Chapter 1
Nature of Probability and Statistics
Qualitative variables can be placed into distinct categories according to some
characteristic or attribute.
Quantitative variables are numerical in nature and can be ordered or ranked.
Quantitative variables can be further classified into two groups.
o Discrete variables assume values that can be counted.
o Continuous variables can assume all values between any two specific values.
(Discuss boundaries: ex. recorded height of 73 has boundary of 72.5 ≤ x < 73.5 )
Levels of Measurement:
Variables are classified by how are organized, counted, or measured:
Nominal—classifies data into mutually exclusive (nonoverlapping), exhausting categories
in which no order or ranking can be imposed on the data.
Ordinal—classifies data into categories that can be ranked; however, precise differences
between the ranks do not exist.
Interval—ranks data, and precise differences between units of measure do exist;
however, there is no meaningful zero.
Ratio—possesses all the characteristics of interval measurement, and there exists a true
zero.
Data Collection and Sampling Techniques
Surveys are the most common method of collecting data. Three methods of surveying
are:
o Telephone surveys
o Mailed questionnaire surveys
o Personal interviews
Direct Observations or surveying records
Methods to obtain unbiased samples:
o Random samples are selected using chance methods or random methods.
o Systematic samples are obtained by numbering each subject of the population
and then selecting every kth number.
o Stratified samples are obtained by dividing the population into groups according to
some characteristic that is important to the study, then sampling from each group.
o Cluster samples are obtained by using intact groups called clusters.
Two main ways to classify statistical studies:
In an observational study, the researcher merely observes what is happening or what
has happened in the past and tries to draw conclusions based on these observations.
In an experimental study, the researcher manipulates one of the variables and tries to
determine how the manipulation influences other variables.
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M227
Chapter 1
Nature of Probability and Statistics
Statistical studies usually include one or more independent variables and one dependent
variable.
The independent variable in an axperimental study is the one that is being manipulated by
the researcher. The independent variable is also called the explanatory variable. The
rsultant variable is called the dependent variable or the random outcome.
Uses and Misuses of Statistics
Detached statistics
Implied connections
Misleading graphs
Faulty survey questions
Computers and Calculators
In the past, statistical calculations were done with pencil and paper. However, with the
advent of calculators, numerical computations became easier.
Excel, MINITAB, and the TI-83 graphing calculator can be used to perform statistical
computations.
Students should realize that the computer and calculator merely give numerical answers
and save time and effort of doing calculations by hand.
SUMMARY
The two major areas of statistics are descriptive and inferential.
When the populations to be studied are large, statisticians use subgroups called
samples.
The four basic methods for obtaining samples are: random, systematic, stratified, and
cluster.
Data can be classified as qualitative or quantitative.
The four basic types of measurement are nominal, ordinal, interval, and ratio.
The two basic types of statistical studies are observational and experimental.
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