SECTION 1.1 - INTRODUCTION TO THE PRACTICE OF STATISTICS

SECTION 1.1 - INTRODUCTION TO THE PRACTICE OF STATISTICS Definition Statistics is the science of collecting, organizing, summarizing, and analyzing information (data) to draw conclusions or answer questions. In addition, statistics is about providing a measure of confidence in any conclusions. Definitions The entire group of individuals to be studied is called the population. An individual is a person or object that is a member of the population being studied. A sample is a subset of the population that is being studied. Definitions A statistic is a numerical summary of a sample. A parameter is a numerical summary of the population. Example 1 Use the Gallup Poll Americans Divided About Future Gulf Drilling to answer the following questions. a.

What is the population?

b.

What is the sample?

c.

The article indicates that 46% think that BP should not be allowed to drill again in the gulf. Is this a statistic or a parameter? Why?

Definitions Descriptive statistics consist of organizing and summarizing data. Descriptive statistics describe data through numerical summaries, tables, and graphs. Inferential statistics uses methods that take a result from a sample, extend it to the population, and measure the reliability of the result. The Process of Statistics 1. Identify the research objective. 2. Collect the data needed to answer the question(s) posed in (1). 3. Describe the data. 4. Perform the inference.

Definition Variables are the characteristics of the individuals within the population. Definitions Qualitative, or categorical variables allow for classification of individuals based on some attribute or characteristic. Quantitative variables provide numerical measures of individuals. Arithmetic operations such as addition and subtraction can be performed on the values of a quantitative variable and will provide meaningful results. Example 2 Using the survey given out at the beginning of class, classify each of the variables as either qualitative or quantitative. a.

job/profession

b.

number of pets

c.

courses completed

Definitions A discrete variable is a quantitative variable that has either a finite number of possible values or a countable number of possible values. The term countable means that the values result from counting, such as 0, 1, 2, 3, and so on. A continuous variable is a quantitative variable that has an infinite number possible values that are not countable. Example 3 Using the survey given out at the beginning of class, classify each of the quantitative variables as either discrete or continuous. a.

number of pets.

b.

distance traveled to come to class.

Definitions • A variable is at the nominal level of measurement if the values of the variable name, label, or categorize. In addition, the naming scheme does not allow for the values of the variable to be arranged in a ranked or specific order. • A variable is at the ordinal level of measurement if it has the properties of the nominal level of measurement and the naming scheme allows for the values of the variable to be arranged in a ranked or specific order. • A variable is at the interval level of measurement if it has the properties of the ordinal level of measurement and the differences in the values of the variable have meaning. A value of zero in the interval level of measurement does no mean the absence of the quantity. Arithmetic operations such as addition and subtraction can be performed on values of the variable. • A variable is at the ratio level of measurement if it has the properties of the interval level of measurement and the ratios of the values of the variable have meaning. A value of zero in the ratio level of measurement means the absence of the quantity. Arithmetic operations such as multiplication and division can be performed on the values of the variable. Example 4 Using the survey given out at the beginning of class, identify the level of measurement for each of the following variables. a.

number of pets.

b.

distance traveled to come to class.

c.

job/profession