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# Chapters 1 and 2 Math 217

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This 4 page Class Notes was uploaded by chrt@iup.edu Notetaker on Friday September 11, 2015. The Class Notes belongs to Math 217 at Indiana University of Pennsylvania taught by Russell S. Stocker in Summer 2015. Since its upload, it has received 10 views. For similar materials see Probability and Statistics in Math at Indiana University of Pennsylvania.

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Date Created: 09/11/15

Probability and statistics Chapters 1 and 2 De nitionl Statistics is the science of collecting organizing summarizing and analyzing information to draw conclusions or answer questions De nition 2 A population is the entire collection of individuals or objects to be considered or studied De nition 3 A study that utilizes all individuals in a population is called a census Why we don t always use census 1 Logistics Time Money Size of Work Force 2 Missing Information 3 Wrong Conclusions De nition 4 A Sample is a subset of the entire population 0 We want our samples to be as representative as possible in terms of population 0 We often work with samples instead of populations De nition 5 A Parameter is a numerical summary of a population De nition 6 A Statistic is a numerical summary of a sample Statistics are often used to make statements about parameters De nition 7 Descriptive statistics are graphical and numerical methods use to describe organize and summarize data De nition 8 lnferential statistics are techniques and methods used to analyze a speci c set of data in order to draw a conclusion about a population De nition 9 A Sample frame is a list of all the individual or units in the population that we will draw out sample from EX 1 According to a New York Times Article quot For Exercise in New York Futility Push Buttonquot 77 of the 3250 walk buttons in New York City do not work Population 3250 walk buttons Sample None Taken Statistic No Statistic cause no sample Parameter 77 of walk buttons do not work 2 A researcher is interested in the average Weight of all bass in a lake They take a map of the lake and split it into 1000 regions A random sample of 50 regions is taken and within each region they catch 5 different fish The average weight of the fish for all regions is 67 lbs Population All bass in Lake Sampling Frame 1000 regions Sample 50 region 250 bass Statistic Average weight 250 bass 67 lbs Parameters of Interest Average Weight of all bass in the lake De nition 10 Probability sampling is the process is the process of using chance to select individuals from a population to be included in the sample Simple Random Sampling 0 We are taking a sample of size n from a population of size N 0 Simple random sampling occurs when all samples of size n are equally likely to occur 0 Simple random sampling is the back bone of the different types of sampling designs De nition 11 A Variable is a characteristic of an individual or object in a population of interest De nition 12 Qualitative variables allow for classi cation of individuals based on some attribute characteristic Another term for a qualitative variable is a categorical variable De nition 13 Quantitative variables provide numerical measures of individuals mathematical operations can be performed on the values of the quantitative variable and provide meaningful results Another Term for a quantitative variable is a numerical variable Ex Classify the following as qualitative or quantitative variables a Nationality of individual Qualitative b Number of children in a family Quantitative c A person s telephone number Qualitative d A college student s academic standing Qualitative e A person s age Quantitative De nition 14 A discrete variable is a quantitative variable that either has a nite number of possible values of a countable number of possible values The term countable means the values from counting such as 0123 and so on De nition 15 A continues variable is a quantitative variable that has an in nite number of possible values it can take on and can be measured to any desired level of accuracy an uncountable number of possible values De nition 16 The list of observations a variable assumes is called data De nition 17 Qualitative data are observations corresponding to a qualitative variable De nition 18 Quantitative data are observations corresponding to a quantitative variable 0 While gender is a variables the observations male female are the data Ex Give the possible values and classify the following quantitative variables being either discrete or continuous variables 1 The number of cars that cross an intersection in a given day Possible Values 0 1 2 3 countable of possible values Discrete 2 The Temperature outside at 12 PM Possible Values Any Temp Above Absolute O uncountable of possible values Continuous 3 The amount of soda in a 12 ounce can Possible Values O125 Uncountable value of possible values conUnuous 4 The number of whole days it takes before having a recurrence ofcancen Possible value 12 3 4 countable number Discrete Variable

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