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Lesson 1:  Looking at Data:  Distributions

Contents

This lesson covers ...

• Objectives
• Key Terms
• Reading Assignment
• Internet Links
• Study Questions
•  Study Notes
• Written Assignment

Objectives

After completing this lesson, you should be able to:

1. Construct and interpret graphical displays of the distribution of a dataset.
2. Compute and interpret appropriate numerical summaries of a distribution.
3. Use the normal distribution to describe important features of a dataset.

Reading Assignment

Read Chapters 1 in Introduction to the Practice of Statistics 

Key Terms

• Distribution
• Skewness
• Outlier
• Stemplot
• Histogram
• Boxplot
• Dotplot
• Measures of Center
• Mean
• Median
• Measures of Spread
• Quartiles
• Standard Deviation
• Normal Distribution
• Standard Normal Distribution

Internet Links

Each day you go online, be sure to check out the Random Statistical Quote for the Day
  Investigate the following examples from other Internet sites:

• Statsoft's Site Take a look at Basic Statistics, shape of distributions for a nice presentation of the ideas
• UCLA Electronic Text  Take a look at topics 1,2,4, and 5 for this lesson.
• UCLA Electronic Text, Variation.  This section at UCLA concerns measures of variation.
• UCLA XLISP-STAT Demos.  Examine Section 3, modules 2 and 3.  You will need to set up the software xlispstat to be a helper application to do these.  Follow instructions on this page to get xlispstat and to designate it as a helper application.   These modules are very cool.  It is worth getting the software and doing all the setup.
•   Normal Distribution module by David Stockburger  This fantasy provides a nice introduction to dealing with data in a "real" situation.
• Summarising and Presenting Data from SurfStat.australia  Explore the modules at this site for displays, numerical summaries, and normal distributions.

Study Questions

1. What things would a histogram reveal that would be missing in a boxplot?
2. What measure of spread should you use if there was a really nasty outlier?
3. What measure of center should you use if the data were skewed right?
4. What measure of spread would be appropriate if the data had a nice, bell-shaped distribution?
5. What proportion of measurements would be greater than 1 in a normal curve with mean mu=2, and standard deviation sigma=1?
6. What is the 95th percentile of a normal distribution with mean mu=100 and standard deviation, sigma=10?

Study Notes

This format has been too slow and cumbersome on my computer, if you have the same experience, try the html version of the notes in the link below.

Lesson 1 Notes (HTML Format) Lecture notes from Chapter 1.

Lesson 1 Activities

Do the following activity, but don't worry about submitting it, the submit button doesn't send it anywhere.

• MATCHING NUMERICAL & GRAPHICAL REPRESENTATIONS: standard deviation

Statistics Computing

STATLETS Program Access Here

After clicking the link, in the upper left there should be a spinning cube. Just below that cube click menu version Java 1.0. The first time you click this there will be a delay as the program starts. You will then be given a small spreadsheet for you to enter the columns of data. After entering a column of data you can choose the type of analysis you wish to perform. The program is slow the first time it is used on your computer, but should be speedier the next time it is used. Email for help.

The link below takes you to a STATLETS help page we have created. The example screens should help guide you through the data entry and analysis needed for this assignment. The introductory STATLETS screen also has a help system available.

STATLETS Examples Help Page

Written Assignment

Do the following assignment. The problems listed are from the textbook in chapter 1. When you have worked on the problems and are ready to turn in your findings, click the assignment link below. It will take you to a template where you can fill in your answers to the questions. When you are finished entering your answers, click the submit button, you will be given the location of your completed web page.  You may check your assignment responses with your browser at any time, and submit a revision at any time before the due date of the assignment. However, whenever you make a submission, all previously submitted information will be overwritten and therefore lost. It is also perfectly acceptable to submit your written homework solutions to the mail address math1601@cda.morris.umn.edu.

Lesson Submission 1

Due on July 23, 1999 (Friday)

Text problems 1.18, 1.53, 1.57, 1.80, 1.87, 1.88, 1.96

Assignment #1.