MAT 209 - Statistics Chapter 1 - Introduction to Statistics

Statistics: A First Course 8th Ed.
Freund & Perles

Chapter 1 Introduction

Statistics: A branch of mathematics dealing with data collection, organization, analysis, interpretation and presentation.

Data: Facts and statistics collected together for reference or analysis.

Central Tendency: (Or measure of central tendency) is a central or typical value for a probability distribution. It may also be called a center or location of the distribution.

Statistics Subheadings (Branches off original origins of government census and games of chance):

·      Descriptive statistics - A summary statistic that quantitatively summarizes basic features of a collection of information.

·      Inductive statistics - Branch of statistics dealing with conclusions, generalizations, predictions, and estimations based on data from samples

·      Probability theory - Branch of mathematics that deals with quantities having random distributions.

1.1, 1.2 Data Types

·      Numerical data – Data that contains numbers that can be treated by ordinary arithmetical methods.

·      Categorical data – Data that is sorted into non-numerical categories.

·      Nominal data – Data that is used to label variables without providing any quantitative value. It is the simplest form of a scale of measure. Cannot be manipulated using available mathematical operators. (Mathematical operators =, ≠; measure of central tendency = mode)

·      Ordinal data – Data type where the variables have natural, ordered categories and the distances between the categories is not known. (Mathematical operators >, <; measure of central tendency = mode, median)

·      Interval data – Data type, which is measured along a scale, in which each point is placed at equal distance from one another. (Mathematical operators +,-; measure of central tendency = mode, median, mean, standard deviation)

·      Ratio data – Quantitative data, having the same properties as interval data, with an equal and definitive ratio between each data and absolute “zero” being a treated as a point of origin. (Mathematical operators *,/; measure of central tendency = mode, median, arithematic mean, geometric mean, and coefficient of variation)

1.3 Populations & Samples

·      Population – Total set of observations that can be made.

·      Sample – Partial/parts of original observations made. à (Population > sample)

1.4 Data Bias

·      Possibility of bias in methods of data collection: personal interviews, telephone calls, and or mail questionnaires.

1.5, 1.6, 1.7 Statistics in the Textbook Overview

·      Increasing quantitative approach in all fields of research and business = more statistics.

·      Large quantity of statistics can be used to mislead with bias à 5 W’s important.

·      Textbook is a general statistics book à preps student for further specialization.

·      Rise in emphasis from summarizing to making inferences

·      Decision theory – Study of the reasoning underlying an agent's choices. Can be broken into two branches: normative decision theory, which gives advice on how to make the best decisions given a set of uncertain beliefs and a set of values, and descriptive decision theory which analyzes how existing, possibly irrational agents actually make decisions.

·      Exploratory data analysis – Approach to analyzing data sets to summarize their main characteristics, often with visual methods. 

Statistical “W’s”

·      Who was the data about?

·      What was being collected about this object?

·      Where was the data collected?

·      When was the data collected?

·      How was the data collected?