Stat 1000 Tips for Assignments about Density Curves and the Normal Distribution
Published: Tue, 10/19/10
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Throughout the term I will send you all sorts of tips to help you study and learn the course. You probably already have done so, but, if not, I strongly recommend you purchase my Basic Stats 1 Study Book. You will find it a great resource to learn the course. I pride myself in explaining things in clear, everyday language. I also provided numerous examples of all the key concepts with step-by-step solutions. You can order my book at UMSU Digital Copy Centre at University Centre at UM campus. They make the book to order so please allow one business day. The book is split into two volumes and each volume costs $45 + tax.
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Tips for Assignments about Density Curves and the Normal Distribution
For those of you using Web Assign these tips refer to HW4. If you are taking the course by distance/online, these tips relate to your HW3. If you are doing good old-fashioned paper hand-in assignments, these tips will help you with the first half of Assignment 3; you will also want to see my tips on Probability that I will send later this week.
Study Lesson 2 in my book, if you have it, to prepare for this assignment.
Note, a "cumulative proportion" is a left area on the bell curve. Cumulative proportion is P(Z < z). If you are asked to find a cumulative proportion, you want to determine the left area. If you are given the cumulative proportion, you are given a left area.
For those of you in Distance Ed, do not use CrunchIt! in the problems that tell you to. You are using JMP 8 in this course. CrunchIt! is no longer able to do some of the things they ask, so you may as well not bother using it at all.
For the JMP 8 part of the Web Assign assignment, here are some tips:
Open a "New Data Table" in JMP. To copy and paste the data into JMP, in the toolbar at top select "Edit" then "Paste with Column Names". Double-click the "gpa" column heading and make sure the Data Type is Numeric and the Modeling Type is Continuous, using the drop-down menus to fix that if necessary. Double-click the "sex" column heading and make sure the Data Type is Character and the Modeling Type is Nominal, using the drop-down menus to fix that if necessary. Click OK.
To get side-by-side boxplots: In the toolbar at the top, select Analyze then select Fit Y By X. In the pop-up menu, highlight the gpa column and click the Y, Response button. Highlight the sex column and click the X, Factor button. Click OK. You will then see a graph with a vertical array of dots for the males (1) and the females (2). Click the red triangle next to "Oneway Analysis ..." and select "Display Options". You will then be able to select "Box Plots" in the Display Options sub-menu.
To get normal quantile plots: Click the red triangle and select the option Normal Quantile Plot. Choose "Plot Actual by Quantile" in the sub-menu. This portrays the normal quantile plot for the males and females on the same graph, but colour codes which plot is for which sex.
But, they want you to make a normal quantile plot for the males and a separate plot for the females, you have to do it this way:
In the toolbar at the top, select "Analyze" , then "Distribution". In the pop-up menu, highlight "gpa" and click "Y, Column". Highlight "sex" and click "By". Click OK. You now see separate histograms for the males and for the females. Click the red triangle next to "gpa" for both the males and for the females, and select "Normal Quantile Plot" to get a separate normal quantile plot for the males and females.
A normal quantile plot checks to see if a sample's distribution appears to be normal. If the data follows a normal distribution, the normal quantile plot will look like a rising diagonal line. If the plot looks curved rather than linear, there is evidence the data is not normal. However, none of that seems to matter in your question, all they ask is which students are clear outliers, which, personally, I think is much easier to see from your side-by-side boxplots than from your normal quantile plots.