Statistics
Data
numeric values that are gathered through measurements and/or observations.
Data Set
a collection of data values
Data Value (datum)
an individual value in a data set
Population
Entire group to be studied
Ex: people, animals, foods,
Individual
person or object that is a member of the population being studied
Sample
is a subset of the population that is being studied
Statistic
numerical summary of a sample
Descriptive statistics
consist of organizing and summarizing data. Described data through numerical summaries, tables, and graphes.
Examples include: the U.S. Census, Special Interest, Group Studies, Marketing Studies, Consumer
Habits, etc
Inferential Statisitics
uses methods that take a result from a sample, extend it to the population, and measure the reliability of the result.
Ex: Games of chance, insurance industry, simulations, consumer taste,
Parameter
numerical summary of population
Process of Statistics
1. Identify the research objective: A researcher must determine the questions he or she wants answered. The questions must be detailed so that it identifies the population that is to be studied.
2. Collect the data needed to answer the questions posed in #1
3. Describe the data
4. Perform Inference: Apply 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, or categorical, variables
allow for classification of individuals based on some attribute or characteristic
Examples are: gender, geographic area, religious affiliation, membership in a group, etc
Quantitative variables
provide numerical measures of individuals. The values of a quantitative variable can be added or subtracted and provide meaningful results.
Examples : age, weight, height, GPA, IQ, distance, payments, tax owed, etc.
Approach
way to look at and organize a problem so that it can be solved
Discrete Variable
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, 1,2,3. A discrete variable cannot take on every possible value between any teo possible values.
Examples: # of Baseball Games won by the Cardinals , # of members of a family, # of students in a class, # of leaves on a tree, # of digits in a zip code, # of stars in the galaxy, # of people who wear glasses, etc.
Continuous Variable
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.
Examples: a person's temperature, distance between two places, the speed of an object, time, amount of force applied, etc
Nominal level of measurement
if the values of the variable name, label, or categorize. In addition, the naming sceme does not allow for the values of the variable to be arranged in a ranked or specific order.
EX: Grouping people by their nationality, gender, their religion, zip code of residence, marital status, etc.
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
Ex: Letter Grades ( A, B, C, D, & F); Rating Scales ( Outstanding, Excellent, Good, Average, Poor, Unsatisfactory); Rankings ( General, Colonel, Captain, Sergeant , Corporal, Private)
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 foes not mean the absence of the quanitity. Arthmetic operations such as addition and subtraction can be performed on values of the variable.
EX: IQ may be 100 or 110 ( An IQ of zero does not exist), Temperature may be 90 or 91 degrees ( 0 temperature does not mean no heat)
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 varibale.
Ex: (Examples include height, weight, area, # of phone calls, etc.)
Random variable
is one whose values are determined by chance
Independent variable
is one whose value is chosen free of any influence by the value of other variables or any given situation
Dependent variable
is one whose value is determined by the value held by another variable at a given time.
Grams of carbohydrates in a doughnut
Quantitative
Number of unpopped kernals in a bag of ACT microwave popcorn
Quantitative
Phone number
Qualitative
Goals scored in a season by a soccer player
Discrete
Length (in minutes) of a country song
Continuous