What Are Statistics and What are They Used For?

Statistics is the science of collecting, organizing, summarizing, analyzing, and making inferences from data. The practice of statistics takes data from a population and describes it in a meaningful way, so that conclusions can be drawn or predictions and/or decisions made. Statistics is divided into two types o Descriptive statistics o Inferential statistics

Two General Types of Statistics Descriptive statistics Collects, organizes, and summarizes data Inferential statistics Determines relationships, makes predictions, draws inferences

Data & Variables Data are values or measurements. Data are collected from observing variables. Variables are factors that can be changed or that can be observed to be changing in nature.

Types of Data Quan titative data are values that are numeric. Examples: Qual titative data are descriptive but not numeric. Examples: Which one can be described more objectively?

Types of Variables Independent variables are manipulated by experimenters or are what is changing in the natural world. Dependent variables change as independent variables are manipulated or as they change. A change in the independent variable directly causes a change in the dependent variable. On graphs, the x-axis displays the independent variable, and the y-axis displays the dependent variable.

X-axis (Independent Variable) = Change in Year Y-axis (Dependent Variable) = Number of Tadpoles Number of tadpoles is dependent on the year.

Population: An Important Term to Know In this class, we will use the term “population” in two different ways. Biologically —A group of individual organisms of the same species living in the same area at the same point in time Example : The population of coyotes living within the Cottonwood city limits Statistically —All the elements being studied at a particular time Example : The ACT math cores for Mingus High in 2012

How Are Samples Used in Statistical Analyses? Often population numbers are huge, and it would not be practical to measure or count all members. A sample is a decided subset of the whole population used to represent the population as a whole. Have you every been asked to participate in a national poll? If so, you are part of a sample, which might be used to predict or describe a phenomenon of American life. Questions might arise about whether a sample is “random” or not or if the sample size is robust. The answer to these questions could determine the validity of the resulting conclusions.

Uncertainty & Probability When you come close to an intersection, and the traffic light has just changed to amber, you need to make a decision about whether you can make it through the intersection before the light turns red. You might be uncertain of the outcome. You might think that you will probably make it through before the light turns red, but you still have some doubt.

Probability is Related to Uncertainty If the chance of making it through the intersection before the light turns red is converted into a number (science likes numbers!), it would be represented as Number of Favorable Outcomes (Make it Through) Total Number of Possible Outcomes (Make it Through or Don’t Make it Through) = ½ or 0.5