fundamentals of statistics 5th edition
What is statistics?
Statistics is a very broad subject, with applications in a vast number ofDifferent fields. In generally one can say that statistics is the methodology
for collecting, analyzing, interpreting and drawing conclusions from information.
Putting it in other words, statistics is the methodology which scientists
and mathematicians have developed for interpreting and drawing conclusions
from collected data. Everything that deals even remotely with the collection, processing, interpretation and presentation of data belongs to the Domain of statistics, and so does the detailed planning of that precedes all These activities.
BASIC FUNDAMENTAL Definition Of Statistics
Statistics consists of a body of methods for collecting and analyzing data.Some questions that could be answered by statistical method of data collection
- What kind and how much data need to be collected?
- How should we organize and summarize the data?
- How can we analyze the data and draw conclusions from it?
- How can we assess the strength of the conclusions and evaluate their
That is, statistics provides methods for
- Design: Planning and carrying out research studies.
- Description: Summarizing and exploring data.
- Inference: Making predictions and generalizing about phenomena represented
BASIC FUNDAMENTAL CONCEPTS OF STATISTICS
- POPULATION AND SAMPLE
- DESCRIPTIVE AND INFERENTIAL
Population and sample are two basic concepts of statistics. Population can
be characterized as the set of individual persons or objects in which an investigator
is primarily interested during his or her research problem. Sometimes
wanted measurements for all individuals in the population are obtained, but
often only a set of individuals of that population are observed; such a set of
individuals constitutes a sample. This gives us the following definitions of
population and sample.
Definition of Population. Population is the collection of all individuals
or items under consideration in a statistical study. (Weiss, 1999)
Definition of Population. A (statistical) population is the set of measurements (or record of some qualities trait) corresponding to the entire collection of units for which inferences are to be made. (Johnson & Bhattacharyya,
1992)
Definition of Sample. Sample is that part of the population from which
information is collected. (Weiss, 1999)
Definition of Sample. A sample from statistical population is the set of
Measurements that is actually collected in the course of an investigation.
(Johnson & Bhattacharyya, 1992).
When population and sample is defined in a way of Johnson & Bhattacharyya,
then it’s useful to define the source of each measurement as sampling unit,
or simply, a unit. Also We learn about the population by sampling from the collection.
Example of Finite population. In many cases the population under consideration
is one which could be physically listed. For example:
–The students of the University of Tampere,
–The books in a library.
Example of Hypothetical population. Also in many cases the population
is much more abstract and may arise from the phenomenon under consideration.
Consider e.g. a factory producing light bulbs. If the factory keeps
using the same equipment, raw materials and methods of production also in
future then the bulbs that will be produced in factory constitute a hypothetical
population. That is, sample of light bulbs taken from current production
line can be used to make inference about qualities of light bulbs produced in
future.
Descriptive and Inferential Statistics
There are two major types of statistics. The branch of statistics devoted
to the summarization and description of data is called descriptive statistics
and the branch of statistics concerned with using sample data to make an
inference about a population of data is called inferential statistics.
Definition 1.6 (Descriptive Statistics). Descriptive statistics consist of meth-
ods for organizing and summarizing information (Weiss, 1999)
Definition 1.7 (Inferential Statistics). Inferential statistics consist of meth-
ods for drawing and measuring the reliability of conclusions about population
based on information obtained from a sample of the population. (Weiss, 1999)
Descriptive statistics includes the construction of graphs, charts, and tables,
and the calculation of various descriptive measures such as averages, measures
of variation, and percentiles. In fact, the most part of this course deals with
descriptive statistics.
Inferential statistics includes methods like point estimation, interval estimation
and hypothesis testing which are all based on probability theory.
Example (Descriptive and Inferential Statistics). Consider event of tossing
dice. The dice is rolled 100 times and the results are forming the sample
data. Descriptive statistics is used to grouping the sample data to the following
table
| Outcome of the roll Frequencies in the sample data 1 10 2 30 3 18 4 12 5 19 6 25 |
Inferential statistics can now be used to verify whether the dice is a fair or
not.
Descriptive and inferential statistics are interrelated. It is almost always necessary
to use methods of descriptive statistics to organize and summarize the
information obtained from a sample before methods of inferential statistics
can be used to make more thorough analysis of the subject under investigation.
Furthermore, the preliminary descriptive analysis of a sample often
reveals features that lead to the choice of the appropriate inferential method
to be later used.
Sometimes it is possible to collect the data from the whole population. In
that case it is possible to perform a descriptive study on the population as
well as usually on the sample. Only when an inference is made about the
population based on information obtained from the sample does the study
become inferential.
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