### Statistics Data Variable And Individual Values

This chapter covers statistics data variable and individual values.

Statistics

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

data

a fact or proposition used to draw a conclusion or make a decision. it describe characteristics of an individual

Data can be

numerical, as in height, or nonnumerical, as in gender

Anecdotal means

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

population

The entire group of individuals to be studied

individual

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

sample

is a subset of the population that is being studied.

descriptive statistic

it describes the results of the sample without making any general conclusions about the population consist of organizing and summarizing data. describe data through numerical summaries, tables, and graphs.

statistic

is a numerical summary of a sample

This is an example of what “Suppose 39 of the 50 students stated that they would return the money to theowner.We could present this result by saying the percent of students in the survey that stated they would return the money to the owner is 78%”

Descriptive statistic

Inferential statistics

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

If we extend the results of our sample to the population and say that the proportion of all students at the school who would return the money is 78%, we are performing

Inferential statistics

parameter

is a numerical summary of a population.

Suppose the percentage of all students on your campus that own a car is 48.2%. Is this a statistic or parameter?

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. is this a statistic or parameter ?

This value represents a statistic because it is a numerical summary of a sample.

convenience samples

Many nonscientific studies are based on Internet surveys or phone-in polls. The results of any study performed using this type of sampling method are not reliable.

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 inference

1. Identify the research objective.

A researcher must determine the question(s) he or she wants answered.The question(s) must be detailed so that it identifies the population that is to be studied.

2. Collect the data needed to answer the question(s)

Gaining access to an entire population is often difficult and expensive. When conducting research, we typically look at a sample. The collection of data step is vital to the statistical process, because if the data are not collected correctly, the conclusions drawn are meaningless. Do not overlook the importance of appropriate data-collection processes.

3. Describe the data

Obtaining descriptive statistics allows the researcher to obtain an overview of the data and can provide insight as to the type of statistical methods the researcher should use

4. Perform inference

Apply the appropriate techniques to extend the results obtained from the sample to the population and report a level of reliability of the results.

Variables

are the characteristics of the individuals within the population.

Qualitative

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.

approach

or a way to look at and organize a problem so that it can be solved

Distinguishing between Qualitative and Quantitative Variables (a) Gender

(a) 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.

Distinguishing between Qualitative and Quantitative Variables (b) Temperature

(b) 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.

Distinguishing between Qualitative and Quantitative Variables (c) Number of days during the past week that a college student aged 21 years or older has had at least one drink

(c) Number of days during the past week that a college student aged 21 years or older had at least one drink is a quantitative variable because it is numeric, and operations such as addition and subtraction provide meaningful results.

Distinguishing between Qualitative and Quantitative Variables (d) Zip code

(d) Zip code is a qualitative variable because it categorizes a location. Notice that, even though they are numeric, the addition or subtraction of zip codes does not provide meaningful results.

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.

continuous variable

is a quantitative variable that has an infinite number of possible values that are not countable.

Distinguishing between Discrete and Continuous Variables (a) The number of heads obtained after flipping a coin five times.

(a) The number of heads obtained by flipping a coin five times would be a discrete variable because we would count the number of heads obtained. The possible values of the discrete variable are 1,2,3,4…

Distinguishing between Discrete and Continuous Variables (b) The number of cars that arrive at a McDonald’s drive-through between 12:00 P.M. and 1:00 P.M.

(b) The number of cars that arrive at a McDonald’s drive-through between 12:00 P.M. and 1:00 P.M. is a discrete variable because its value would result from counting the cars. The possible values of the discrete variable are 0, 1, 2, 3, 4, and so on. Notice that there is no predetermined upper limit to the number of cars that may arrive.

Distinguishing between Discrete and Continuous Variables (c) The distance a 2007 Toyota Prius can travel in city driving conditions with a full tank of gas.

(c) The distance traveled is a continuous variable because we measure the distance.

The type of variable (qualitative, discrete, or continuous) dictates

the methods that can be used to analyze the data.

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.

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.

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

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

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.

Determining the Level of Measurement of a Variable. (a) Gender

(a) 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.

Determining the Level of Measurement of a Variable. (b) Temperature

(b) 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.

Determining the Level of Measurement of a Variable. (c) Number of days during the past week that a college student aged 21 years or older has had at least one drink

(c) Number of days during the past week that a college student aged 21 years or older has had at least one drink 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 had four drinks had twice as many drinks as a student who had two drinks.

Determining the Level of Measurement of a Variable. (d) Letter grade earned in your statistics class

(d) 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.

Validity

of a variable or measurement represents how close to the true value the measurement is. In other words, a variable is valid if it measures what it is supposed to measure.\

Reliability

of a variable or measurement represents the ability of different measurements of the same individual to yield the same results

A(n)_____________ is a person or object that is a member of the population being studied

individual

A(n) _____ is a numerical summary of sample. A(n)_____ is a numerical summary of a population.

A(n) statistic is a numerical summary of sample. A(n) parameter is a numerical summary of a population.

determine whether the underlined value is a parameter or a statistic. State Government Following the 2006 national midterm election, 18% of the governors of the 50 United States were female.

parameter

determine whether the underlined value is a parameter or a statistic. Illegal Drugs In a national survey of high school students (grades 9 to 12), 25% of respondents reported that someone had offered, sold, or given them an illegal drug on school property.

statistic

determine whether the underlined value is a parameter or a statistic. Batting Average Ty Cobb is one of Major League Baseball’s greatest hitters of all time, with a career batting average of 0.366

parameter

determine whether the underlined value is a parameter or a statistic. Hygiene Habits A study of 6,076 adults in public rest rooms (inAtlanta,Chicago,NewYork City,and San Francisco) found that 23% did not wash their hands before exiting.

statistic

classify the variable as qualitative or quantitative. Nation of origin

qualitative

classify the variable as qualitative or quantitative. Grams of carbohydrates in a doughnut

quantitative

classify the variable as qualitative or quantitative. Number of unpopped kernels in a bag of ACT microwave popcorn

quantitative

classify the variable as qualitative or quantitative. Phone number

qualitative

determine whether the quantitative variable is discrete or continuous. Runs scored in a season by Albert Pujols

discrete

determine whether the quantitative variable is discrete or continuous Length (in minutes) of a country song

continuous

determine whether the quantitative variable is discrete or continuous Temperature on a randomly selected day in Memphis, Tennessee

continuous

determine whether the quantitative variable is discrete or continuous Points scored in an NCAA basketball game

discrete

determine the level of measurement of each variable. Nation of origin

Nominal

determine the level of measurement of each variable. Volume of water used by a household in a day

Ratio

determine the level of measurement of each variable. Highest degree conferred (high school, bachelor’s, and so on)

ordinal

determine the level of measurement of each variable. Assessed value of a house

Ratio

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