Homework Assignment #4

All homework assignments must typed or legibly handwritten, and must show your name, the assignment number, course number, and the date clearly. Homework is due at the beginning of class on the specified date.

Due Thursday, October 5

Part 1, Text chapter exercises:
ch. 4: #10 (compute median and mode as well)
ch. 5: #4

Part 2, SDA:
Go to the SDA web site and pick a data set to explore (it doesn't have to be the GSS).  Browse the variables in the codebook and select an interval scale variable you have not yet analyzed in previous assignments that you would like to learn more about.  Then use all techniques you know to give a comprehensive description of this variable in terms of central tendency, dispersion, and shape.  To do this, you will need to do the "Frequencies or Crosstabulations" action and follow the procedures you used in previous assignments or were demonstrated for you in the fertility handouts (e.g., selecting the "statistics" box on the "SDA Tables Program" screen).  The "statistics" output may not give you all the information you need to compute some measures, so you will also need to produce a frequency/percentage distribution.  Even though SDA does not include graphical procedures, you should still draw (by hand) a box plot and histogram using the numerical output from SDA.  Report on all appropriate measures of central tendency and dispersion (be inclusive here, not restrictive like the text recommends).  Include with your summary the 10th and 90th percentiles.  When describing the shape of the distribution, be sure to note any special features (e.g., outliers, multimodality, etc.).  Write a summary paragraph for your comprehensive description of the distribution and be sure to include all SDA output and graphical displays you draw.

Part 3, WebStat
Go to the WebStat site and load the "1000 random digits" sample data set.  Plot these data with a histogram or dotplot.  What is the shape of this distribution?  Interpret the meaning of this shape.  Why would you expect random numbers to be distributed in this way?

Part 4:
Go to the "Mean, median, and standard deviation" web site and click on "Begin."  Work on changing the distribution for this exercise like we did in the lab on Tuesday, Sept. 27.  Keep the range fixed and make it so each value has at least one observation (each value has a bar at least "1" tall).  Play around to make standard deviation as large and as small as you can.  (This may take some time, but it is fun).  What are the features of distributions that have the greatest standard deviations, given the constraints of at least one observation per value?  What are the features of distributions that have the smallest standard deviations?
Draw (by hand) histograms for the distributions you've created with the largest and smallest standard deviations.  There will be a special prize for those who get the highest and lowest standard deviations in the class.

What is the standard deviation when all values have the same number of observations?  Does this change when all values have the same number of observations?