**Module Two Introduction**

Statistical research typically begins with a question that is stated clearly with as much detail as possible so the variable, population, sample, and sampling method can be identified. Then, we begin the study by collecting the data from the participants.

After you have collected the data for a statistical research study, what will you do with it? The data should be organized so we can analyze the information and ultimately reach a conclusion or answer to the research question.

Data can be described and presented in many different formats. In this module, you will study numerical and graphical ways to describe and display the data. This area of statistics is called “*Descriptive Statistics*”. In this module, you will learn how to calculate, and even more importantly how to interpret these measurements and graphs.

**Module 2 Introductory Video**

While the topic may seem out of place, probability is the underlying foundation on which the important methods of inferential statistics are built. You have, more than likely, used probability. In fact, you probably have an intuitive sense of probability. Probability deals with the change of an event occurring. It is often necessary to "guess" about the outcome of an event in order to make a decision.

Politicians study polls to guess the likelihood of winning an election. Teachers choose a particular course of study based on what they think students can comprehend. Doctors choose the treatments needed for various diseases based on their assessment of likely results. You may have visited a casino where people play games chosen because of the belief the at the likelihood of winning is good. You may have chosen your pathway based on the probable availability of jobs. In the second part of this module, you will learn how to solve probability problems using a systematic approach, rather than "guessing".

**Module Two Overview**

- Frequency Distribution for Quantitative Data - Tables & Graphs
- Descriptive Statistics for Quantitative Data
- Measures of Center
- Measures of Variation
- Measures of Position

- Probability Introduction and Binomial Distribution
- Normal Distributions

**COURSE OBJECTIVES**

The student will be able to:

- demonstrate fundamental concepts in exploratory data analysis
- apply the basic concepts of probability and random variables
- describe the concept of the sampling distribution of a statistic and characterize the behavior of the sample means
- communicate and present statistical ideas clearly in oral and written forms using appropriate technical terms and deliver data analysis results to non-statistical audience

**MODULE TWO OBJECTIVES**

The student will be able to:

- explain examples of data set summaries, including common graphical tools (such as histogram, stem and leaf plot, and boxplots) and summary statistics (five number summary, mean, and standard deviation)
- summarize the features that describe a data set or distribution
- use an appropriate software tool for data summary and exploratory data analysis
- interpret basic probability rules
- calculate the probabilities of single events, complementary events, or the unions or intersections of a collection of events
- compute probabilities using two-way contingency tables
- identify the random variable(s) of interest in a given scenario
- contrast discrete and continuous random variables
- determine if a binomial distribution is an appropriate method for a given scenario
- compute probabilities for a binomial distribution
- calculate the mean and standard deviation for a binomial distribution
- for a normal distribution, find the probability over a set of values
- for a normal distribution, find the percentile or specified x-value