Math 151 , Fall 2006, Day 4, Fri., Sept.1 Hit reload to get most current version

HW assignment  Day4  (From Moore unless otherwise noted.)
(Re)Read Ch.2 thru p. 47.  Read 53-55, "Organizing...". Do "check" p. 56,  2.15,17,18 (5#summary/boxplot) Ahead: Finish Ch. 2. ("check" 2.19 (don't calculate. It's not #a), 20, 21, 22)
Hand in Mon: 5# summary, boxplots
p. 45, 2.5 Wood again.  Also make a boxplot.
p. 58, 2.28 U. endowments.  They mean, what do you have to count in to, in the list, to locate the mean and quartiles?
p. 58, 2.29 fruit eating
p. 58, 2.30 newborns.  (I said I wouldn't make you make a histogram, but the data's already pre-binned, so do it here.) Describe the distribution--symmetric, skewed?
p. 59,2.34 guinea pigs survival:  For a) use the One Variable Statistical Calculator Applet at  http://www.whfreeman.com/bps  (It's in the datasets as if for BPS3e; ex02-23.dat) or on your text's CD.  Just observe the skewness.  For b), find the 5-number summary (easy since they're in order in the book), check your answers with the Applet results.  Draw the boxplot and compare with the histogram on your screen.  (with or without outliers, I don't care.)
p. 60, 2.35  days of births, CA The book's question is very open-ended.  Answer instead the questions just below*
 		"Read," to discuss (be able to answer in class)



Optional 
play, with Applet)
* Questions for 2.35, p. 60:
A.  a) Which day had the lowest Median (and about what was that number)?
     b) Which day had the highest Median (and about what was that number)?
      c) Which day had the highest variability (spread), measured by:
                     --IQR (about what are the quartiles for this day)?
                     --Range (about what are min and max for this day)?
       d) Tuesday appears to be somewhat skewed.  Left, or Right skewed?
B.  Compare the Canadian with the American data (p. 10):
    a) Is the general pattern the same in the Canadian and American data?  Discuss briefly the common findings.
    b)(Following the 4-step method, p. 53:) State the issue: Is the weekend/weekday difference greater in Canada or the US (or are they similar?)  Formulate an appropriate answer: Find the percent of Tuesday's births (median for CA, total for US) that Sunday has.  Solve:  Take the number for Sunday, divide by Tuesday's number, restate as a percent.  Conclude, something like this:  " In Canada, on Sunday(s), the number of births was ___% of the number of births on Tuesday. In US (the parallel statement.)  Therefore the difference is greater in _________.  This may indicate that proportionately more planned births occur in __________.
    c)  The picture for 2.35 makes the difference between weekdays and weekend days look more extreme than it actually is.  Why/how?
Math151@wells.edu is up.  If you didn't get the welcome message, contact me asap!  Class members also linked from homepage
Clinic hours aren't arranged yet. Jennifer O'Neill (joneill@wells.edu)  Email her to arrange to meet, between now and Mon.
Introduce yourself to at least 2 other people in the class.  Check HW with neighbors.
Wednesday we'll start SPSS--meet at class time in Mac 101 Computer Lab. (Alternate time: 12:30; sign up Mon.)

Measures of middle  (see Day 3 for details)
  Mean, median:  Mean is sensitive to skewness, outliers, Median is resistant to them.  Symmetric distribution? Mean = median!
Measures of spread (dispersion)  See Day 3 for details)
   Quartiles:  1st quartile Q1: 1/4 below, 3/4 above. = 25th percentile.
             (2nd quartile= median = 50th percentile)
            3rd quartile Q3: 3/4 below, 1/4 above.  = 75th percentile.
        Hand computation (Tukey):  Q's are the medians of the 2 halves.  (Median is a data value? Discard it.)
     Five-number summary:  min, Q1, Median, Q3, max. 
        INTERQUARTILE RANGE = IQR= Q3 - Q1. (9.5 - 4 = 5.5 for both sets from day 3)
                =The range of the middle half of the observations.  Resistant to outliers!

Box (and whisker) plot:  Graphical form of five number summary.
    Especially good for comparing sets of data, conditioned on a categorical variable.
"Plain vanilla--Moore" Draw and label the numerical scale first.  Then mark the five numbers. Finish the picture.
The box spreads over the middle half (Q1 to Q3), the whiskers over the lowest and highest quarters (Min to Q1, Q3 to Max).  Each section shows the spread of 1/4 of the data: the longer the section the thinner the data must be spread in there.   Can "read" skewness.
Demonstration with set of 9. 1 3 | 5 6 6 8 8 | 11 20    5#summ: 1, 4, 6, 9.5, 20
Direction of boxplot?  Vertical or horizontal is a matter of taste. I do horizontal, usually.

  |-----[   |      ]--------------------|
0·········5·········10········15········20

"Showing outliers" p.45ff. Outliers can make a boxplot whisker extend deceptively beyond the bulk of the data.
      Make the whiskers to the last item in the "main mass" of the data.
       Put a dot or a star for each outlier,  beyond the whisker end.
   How do we decide what's an outlier?  By hand; use your judgement.
     (Rule of thumb: Knowing rule is optional--used by computers) Define "outlier" as a value farther out than 1.5 IQR  from the Quartiles.
          (Q1 - 1.5 IQR is lower "fence", Q3 + 1.5 IQR is upper "fence".)
                For the set of 9, 1.5 IQR = 1.5×5.5. = 8.25. Fences are 4 - 8.25 = -4.25, and 8 + 8.25 = 16.25.
                   So 20 lies outside the fence, and the whiskers & box  should go from 1 to 11 (largest inside the fence)
        (Dot or *?  Tukey:  Dot ·between 1.5 and 3 IQR's out, * if more than 3 IQR's out. By hand, I don't care.)

  |-----[   |      ]--|                 *
0·········5·········10········15········20 
   This is the same as we would have done without the rule, probably.

Example:  p.60, 2.34 Guinea pig survival: (redo for hw)
Use the One Variable Statistical Calculator Applet at  http://www.whfreeman.com/bps
   Compare boxplot with histogram:  longer boxplot sections mean lower histogram height and vice versa.

Next: Standard deviation.
Sievers home  Math151-Fall06/Daym4.htm  5pm 8/31/06
This page belongs to Sally Sievers who is solely responsible for its content. Please see our statement of responsibility.