# Nature of Probability and Statistics

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. 1 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. 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. 2 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.