Statistics

Statistics

than none of A can occur. With this, there will be some outcomes for B that will not influence A. • Randomness: All outcomes have the same probability of being chosen or occurring. If you randomly ask people on a street to answer a survey question, given all other factors are equal (meaning that the street is not comprised of a single population, e.g., all male) then you would expect your surveys outcome to represent a random sample of the population. • Population: A population is an entire group, collection or space of objects that we want to characterize. • Sample: A sample is a collection of observations on which we measure one or more characteristics. Frequently, we use (small) samples of (large) populations to characterize the properties and affinities within the space of objects in the population of interest. For example, if we want to characterize the US population, we can take a sample (poll or survey) and the summaries that we obtain from the sample (e.g., mean age, race, income, body-weight, etc.) may be used to study the properties of the population, in general. • Variable: A variable is a characteristic of an observation that can be assigned a number or a category. For instance, the year in college (variable) for a student (observational unit). Appropriate classification of process and variable types are important because they directly influence our decision on how to collect, explore, analyze and interpret data and results. For example, we can carry arithmetic (e.g., average) on quantitative variables, but we need to analyze frequencies of occurrence for qualitative variables. There are two types of variables: categorical and quantitative. These types of variables can be split further. • Categorical: Categorical variables are qualitative measurements of samples or populations that are classified into groups: o Ordinal categorical variables are qualitative descriptions that have a natural arrangement or order of the measurements; e.g., rank in college (freshman, sophomore, junior, senior), size of soda (small, medium, large), etc. o Not ordinal (or nominal) variable is a categorical variable that does not have a naturally imposed (or meaningful) order of its values; e.g., gender, race, political affiliation (democrat, republican, independent, green party, other), etc. • Quantitative: Quantitative variables are measurements that have a meaningful numerical value representation. There are two types of quantitative variables: o Continuous variables indicate numerical observations that contain intervals with infinite (uncountable) possible values; e.g., weight, height, time, speed, etc. o Discrete variables are also numerical measurements, but they are sparse in space and any interval will contain at most many possible values; e.g., number of students in a school, number of rational numbers in a given interval [a; b], age, etc. 4.2 Types of Variables

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