Statistics 1.1 Introduction to the Practice of Statistics

Anecdotal

the information being conveyed is based on casual observation, not scientific research.

population

The entire group to be studied

Data

The list of observed values for a variable

statistic

a numerical summary of a sample

continuous variable

a quantitative variable that has an infinite number of possible values that are not countable. A continuous variable may take on every possible value between any two values. If you measure to get the value of a quantitative variable, it is continuous.

sample

a subset of the population that is being studied

parameter

is a numerical summary of a population

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 means the absence of the quantity. Arithmetic operations such as multiplication and division can be performed on the values of the variable

Continuous data

are observations corresponding to a continuous variable.

What are the two types of quantitative variables?

discrete and continuous

ordinal level of measurement

if it has the properties of the nominal level of measurement, however the naming scheme allows for the values of the variable to be arranged in a ranked or specific order. ***When you see the word ordinal, think order.

Qualitative data

observations corresponding to a qualitative variable

Quantitative data

observations corresponding to a quantitative variable

Quantitative variables

provide numerical measures of individuals. The values of a quantitative variable can be added or subtracted and provide meaningful results.

What are two types of variables?

qualitative or quantitative

Inferential statistics

uses methods that take a result from a sample, extend it to the population, and measure the reliability of the result.

Qualitative, or categorical, variables

allow for classification of individuals based on some attribute or characteristic. ***Just because the value of a variable is numeric does not mean that the variable is quantitative. For example a zip code

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 does not mean the absence of the quantity. Arithmetic operations such as addition and subtraction can be performed on values of the variable.

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. ***The word nominal comes from the Latin word nomen, which means to name

individual

is a person or object that is a member of the population being studied

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 discrete variable cannot take on every possible value between any two possible values. If you count to get the value of a quantitative variable, it is discrete

Statistics

is the science of collecting, organizing, summarizing, and analyzing information to draw conclusions or answer questions. In addition, statistics is about providing a measure of confidence in any conclusions.

Discrete data

observations corresponding to a discrete variable

For each of the following variables, determine the level of measurement: -Gender -Temperature -Number of days during the past week that a college student studied -Letter grade earned in your statistics class

-Gender is a variable measured at the nominal level because it only allows for categorization of male or female. Plus, it is not possible to rank gender classifications. -Temperature is a variable measured at the interval level because differences in the value of the variable make sense. For example, 70°F is 10°F warmer than 60°F. Notice that the ratio of temperatures does not represent a meaningful result. For example, 60°F is not twice as warm as 30°F. In addition, 0°F does not represent the absence of heat. -Number of days during the past week that a college student studied is measured at the ratio level, because the ratio of two values makes sense and a value of zero has meaning. For example, a student who studies four days studies twice as many days as a student who studies two days. -Letter grade is a variable measured at the ordinal level because the values of the variable can be ranked, but differences in values have no meaning. For example, an A is better than a B, but A-B has no meaning

Determine whether the following variables are qualitative or quantitative. Gender Temperature Number of days during the past week that a college student studied Zip code

Gender is a qualitative variable because it allows a researcher to categorize the individual as male or female. Notice that arithmetic operations cannot be performed on these attributes. Temperature is a quantitative variable because it is numeric, and operations such as addition and subtraction provide meaningful results. For example, 70°F is 10°F warmer than 60°F. Number of days during the past week that a college student studied is a quantitative variable because it is numeric, and operations such as addition and subtraction provide meaningful results. Zip code is a qualitative variable because it categorizes a location. Notice that, even though zip codes are numeric, adding or subtracting zip codes does not provide meaningful results

Example 1 - Parameter versus Statistic

Suppose 48.2% of all students on your campus own a car. This value represents a parameter because it is a numerical summary of a population. Suppose a sample of 100 students is obtained, and from this sample we find that 46% own a car. This value represents a statistic because it is a numerical summary of a sample

Variables

are the characteristics of the individuals within the population

Descriptive statistics

consist of organizing and summarizing data. Descriptive statistics describe data through numerical summaries, tables, and graphs.