Module 2: Descriptive Statistics (Chapter 2)
Section outline
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Once you have collected data, what will you do with it? Data can be described and presented in many different formats. For example, suppose you are interested in buying a house in a particular area. You may have no clue about the house prices, so you might ask your real estate agent to give you a sample data set of prices. Looking at all the prices in the sample often is overwhelming. A better way might be to look at the median price and the variation of prices. The median and variation are just two ways that you will learn to describe data. Your agent might also provide you with a graph of the data.
In this chapter, you will study numerical and graphical ways to describe and display your data. This area of statistics is called "Descriptive Statistics." You will learn how to calculate, and even more importantly, how to interpret these measurements and graphs.
A statistical graph is a tool that helps you learn about the shape or distribution of a sample or a population. A graph can be a more effective way of presenting data than a mass of numbers because we can see where data clusters and where there are only a few data values. Newspapers and the Internet use graphs to show trends and to enable readers to compare facts and figures quickly. Statisticians often graph data first to get a picture of the data. Then, more formal tools may be applied.
Some of the types of graphs that are used to summarize and organize data are the dot plot, the bar graph, the histogram, the stem-and-leaf plot, the frequency polygon (a type of broken line graph), the pie chart, and the box plot. In this chapter, we will briefly look at stem-and-leaf plots, line graphs, and bar graphs, as well as frequency polygons, and time series graphs. Our emphasis will be on histograms and box plots.
Image Caption: When you have large amounts of data, you will need to organize it in a way that makes sense. These ballots from an election are rolled together with similar ballots to keep them organized. (credit: William Greeson)
(Content & Image Source: Chapter 2 Introduction, Introductory Statistics, Barbara Illowsky and Susan Dean, OpenStax, CC BY 4.0 License)
Upon completion of this module, you will be able to:2.1 Stem-and-Leaf Graphs (Stemplots), Line Graphs, and Bar Graphs- Display data graphically and interpret data with stemplots.
- Construct other types of graphs and interpret information displayed in: line graphs and bar graphs.
2.2 Histograms, Frequency Polygons, and Time Series Graphs- Display data graphically and interpret data with histograms.
- Construct other types of graphs and interpret information displayed in: frequency polygons and time series graphs.
2.3 Measures of the Location of the Data- Recognize, describe, and calculate the measures of location of data: quartiles and percentiles.
- Compute the five-number summary.
2.4 Box Plots- Display data graphically and interpret box plots.
2.5 Measures of the Center of the Data- Recognize, describe, and calculate the measures of the center of data: mean, median, and mode.
- Compute the mean, median, and mode of grouped frequency.
2.6 Skewness and the Mean, Median, and Mode- Recognize basic distribution shapes.
2.7 Measures of the Spread of the Data- Recognize, describe, and calculate the measures of the spread of data: variance, standard deviation, and range.
- Use the mean and the standard deviation to calculate z-scores and the empirical rule.
To achieve these objectives:- Read the Module 2 Introduction (see above).
- Read Sections 2.1 - 2.7 of Chapter 2: Descriptive Statistics in Introductory Statistics (links to each Section provided below)
- Complete the MyOpenMath Homework Assignments for the topics in the Chapter (links provided below) - These are graded!
- View the Chapter 2 Review (link provided below)
- Practice the problems in the Chapter 2 Practice and Homework, checking the solutions provided (links to each provided below)
- Submit the Chapter 2 Project: Descriptive Statistics (links to project and submission link provided below)
- Complete the MyOpenMath Quiz for Chapter 2 (link provided below) - This is graded!
- Once you complete the Quiz, upload your work in the Quiz Work Upload Assignment using the submission link below.
- Post in the Chapter 2 Q&A Discussion Forum - link provided below.
Note the check boxes to the right that help you track your progress: some are automatic, and some are manual.Module Pressbooks Resources and Activities
You will find the following resources and activities in this module at the Pressbooks website. Click on the links below to access or complete each item.
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