Elementary Applied Statistics Kathy Ensor, Chair Department of Statistics

What is Statistics? “Statistics is the science of collecting, organizing, and interpreting numerical facts, which we call data”. Pg xxv Based on a “representative sample” what can we say about the population of interest? Use of statistics is pervasive in our society. Examples?

Data? Numerical facts? Numerical summaries of what? Sampling unit - the object or individual on which we are taking a measurement Sampling frame or population - the group from which the sampling units are selected Variable - the characteristic of the sampling unit that we measure

Categorical Variable The sampling unit belongs to one of several groups. Examples? - time for you to speak up! Nominal - No ordering to the categories (blue, red, green, yellow) Ordinal - there is a natural ordering to the categories (excellent, very good, good, …)

Quantitative variable Numerical measures of a variable Examples? Arithmetic operations make sense (adding, dividing…) Ratio and interval scales

Distribution A variable can take on a range of values. The values do not occur in equal numbers “The distribution of a variable tells us what values it takes and how often it takes these values.” Variables exhibit variation; the distribution is the pattern of this variation

Displaying Distributions with Graphs Categorical data Pie charts Bar charts A plot of the count for each category of the variable. What information can you glean from these graphs? Which is the better of the two?

Quantitative Variables Stemplots (stem and leaf plot) Back to back stem and leaf plot describing two variables. Histogram frequency or relative frequency of the number of values of the variable falling into the specified interval.