CS 103 Day 6, Friday April 6, 2001

• Box (and whisker) plot is graphed from the 5-number summary.
• The central box  spans the middle half of the data (from 1st quartile to 3rd quartile, with a line marking the median), and whiskers extend out spanning the outside  quarters (to the min and the max, in the plain vanilla version.)  Inner and outer "fences" are an elaboration..
• Originally conceived of by John Tukey as a pencil&paper device.  Most useful for comparing related packs of data.
• Since each of the 4 segments spans a quarter of the data, a narrower segment means the data is piled higher there, and vice versa.
• Outlier: (p. 75) a number lying outside the pack. The rules of thumb for "moderate", "extreme"  are nice, but not crucial to know.
• Shape: (p. 86)  Skewness is important (kurtosis less so.)
• "Right" skewed = "positive" skewness--longer tail toward bigger numbers.
• Spread (variability)  (p. 86-7, p. 71) IQR is not sensitive to skewness or outliers.

Standard deviation is, very--outliers will pull it disproportionately large.  (Range is very very sensitive.)  Standard deviation is best used only with fairly symmetric distributions without outliers. Works best with "Normal" (bell-shaped, "Gaussian") distributions.
• Middle ("central tendency") again (p. 85-6):

Median is not sensitive to outliers.
Mean will be pulled disproportionately toward long tail or outlier. (Mean is the balancing point of a see-saw holding the data items.)
So Mean will be on the long-tail side of the median in a skewed distribution.
• Logarithm transformation:
• useful in changing a pack of numbers (all >0) which are strongly right (positively) skewed, into a pack more symmetrical.
• It  "shrinks" the distance between very large numbers, the larger the number, the more the shrinking.   The distance between log(10) and log(100) is the same as the distance between log(100) and log(1000) is the same as the distance between  log(1000) and log(10,000)...
• Makes good sense when looking at items as a proportion of other items makes sense. (100 is 10 times 10,  1000 is 10 times 100, 10,000 is 10 times 1000)
• The median (any percentile) of the transformed data is the log of the original median (percentile), but the mean of the transformed data is not the log of the mean of the original data (p. 86.)

• p. 73 Enable Macros (viruses can hide in them, but this is clean.  Watch out for Word documents that unexpectedly have macros)
• p. 73 Boxplot Worksheet: It's hard to see which cells are the range A2:A16.  You just type the numbers into the Data column, leaving no blank cells.  Play around with changing numbers.
• p. 79-80  Errors:  A19 and A22 should be either 1st and 3rd Q (quartile) OR 25th and 75th P (Percentile)
• p. 85-6 Descriptive statistics:  This is the package deal.  There are also separate functions for most all of these (STDEV is standard deviation).

Assignments available as a handout

From Chapter 3, pp. 87-89  Unless otherwise noted, print out and hand in the spreadsheet showing what you created.   Some questions call for written answers based on your examination of the data.  This is just as  important as making the machinery produce the right tables!  You may write on the same page as the  printed spreadsheet.  Assignment 5,  Due Wednesday, April 12 (Day 8, in Week 3)  #1.  Make the boxplot with pencil and paper, by hand!  Do a plain vanilla boxplot.  (boxplot, skewness)  #9a, b.  Boxplots in bunches give a compact way to compare related data sets.         Use the original POLU.XLS file.  Put your boxplot below your data by using "Send output to: Cell: A19".         Stretch the graph sideways so each boxplot is more or less under its column of data.          PRINT OUT the sheet with the data and the boxplots.          For part b:  Describe the general trend in air pollution over time, and discuss the outlier(s).  # 3. all.  (boxplots, sales per employee)  Use the 3WBUS.XLS file from p. 77.      (You don't need any of the things added to the file in the text to do this problem.)      "Sales per $1000” means sales measured in thousands of dollars.  The formula should be      sales/1000 /employees  Assignment 6,  Due Friday, April 14 (Day 9, in Week 3)          Note Percentile(range, percentile) needs the percentile in decimal form--use .20 for 20%, etc. #4 all.  (Baseball) Print histogram, frequency table, boxplot, statistics in part b, and filtered data. (you can do this before you do logarithms, but  hand it in with the rest of  Asst. 6).  #5. (modified)  Transform baseball salary data using the log transformation, making a variable log_salary.  Make and print  a boxplot of the transformed data (log_salary ), compare it to the one in problem 4. Print a histogram for the tranformed data  (log_salary ) Answer 5a and 5b.   Do 4b and 4c (that is, find 10th and 90th percentiles, filter for the players in upper 10%) on the tranformed data  (log_salary).  Do you get the same list of players in the top 10% using log_salary as you got for the original salary data?  Why/why not? #2. a,b,e  (Wisc. business: compare skewness, kurtosis for raw and log data)