Math 151, Spring 2007, Wednesday Jan.31, Day 2  After class

Day 2: Reading: Finish Ch.1, + stemplot  handout, "Check" problems p. 24 1.14, 16 thru 22.  Read ahead in Ch.2 thru p. 47.
Missed class? handouts outside my door, 151 box, white folder

Needed for HW: Stemplot, rounding when there are more than 2 decimal places?  Handout says truncate (round down), Moore text says round to nearest.  Tukey, the inventor, said truncate; throw away the trailing digits; I agree!  This is supposed to be fast--rounding to nearest slows it down.  I encourage truncating but you can do it either way and be right.  If you truncate, your stemplot may look a little different from the text answers. But it will look like a histogram whose bin edges are at the whole numbers.  (A stemplot is hard for a computer to do, but some packages do. For them, rounding to nearest is easiest.  SPSS truncates, which is hard for a computer.)
Do you need to put the leaves in order?  NO, not if you just want the shapes.
Outliers--if they're quite far out, just write the numbers at the bottom (labeled High) or top (labeled Low) e.g. p.20, fig. 1.9, I might write "High 44.2" and stop the stemplot at stem 35.
Hand in (all from Moore text unless otherwise noted). 
p. 28, 1.29 spam  Calculate how much "other" spam there is, and Use your pie template to make a pie chart.  (The pie chart is only "legal" if every item falls into only one box.  I wonder: is a Viagra ad Adult, Health, Leisure, or Products?  Footnote, google: http://www.clickz.com/showPage.html?page=3321901.  Health, I think. )
p. 18, 1.9 foreign born (reading histos)
p.28, 1.30 fruit, 1.31 stocks (reading histos)
p. 31, 1.35 CO2 stemplot.  I would use whole tons as stems, tenths as leaves, see how it looks.  Truncate, don't round, for speed.   Don't bother to put in order.

p. 56, 2.13 (yes.) From this dataset (IQ), make a Dotplot.  Is there anything odd about the data set?  Don't do anything else.

p. 31, 1.34 doctors.   Do a stemplot, not a histogram.  Use hundreds as stems, and split them as on p. 21.
p. 33,1.37 study time back to back, or do side by side on the same scale, like fig. 2.5, p. 55.  (Good stems: maybe by 2's:  80-90, 100-110, 120-130, etc., so stems are 0*, 0t, 0f, 0s,  0., 1*, 1t, 1f, 1s, 1., 2*, 2t etc., and 140 goes on the 1f stem as a 4, 210 goes on the 2* stem as a 1, 30 goes on the 0. stem as a 3, 0 goes on the 0* stem as 0, or is "low".  Splitting by 5's (p. 21) might be good enough. )  Notice the mental rounding of the responses, to quarter hours if not to ten minuteses. Makes "Granular" data.
Read, to discuss 
p.30,1.32 name that variable

p.34,1.40 coins (skewed left)
Optional 
 



Introduce yourself to your neighbors--sides, front & backCheck for Homework questions?
 
Hand in Info sheets, Math pretests if you didn't.   Sign in.  
    If you didn't last time, take your pulse, Pick a card!

Handouts:  Pie template. Stemplot.

Honor code:  This community of learners is a rare and fragile thing.  Trust is the foundation of its structure.  Betraying the trust damages the whole community.  Please do not betray my or your fellows' trust, and I will do my best to reciprocate.  The flip side of this is that if you do betray our trust, I will definitely pursue it in Community Court.

Clinic hours are not all in yet, but our special assistant Anna Radlowski will have her hours
Tues 9:30am-11:00am
Tues 1:30pm-2:30pm
 
Wed 9:30am-10:30am
 
Thurs 9:30am-11:00am
Thurs 1:30pm-2:30pm
Thurs 7:00pm-9:00pm


Data:  Numbers (usually) in context:  What, Who (how many), Why?  When and Where? How?
    Context for height, hair color, shoe size, pulse rate:  Any problems with the way I did it?
    Smoking and brain injury articles?
Variable (possible values), individuals (cases)
         Categorical (ordinal--has natural order or nominal--just names) Ordinal/nominal not in text!
    or Quantitative (can add, average--measured on a ruler-type scale) Units?! ("calories"?)

Distribution of one variable:  what values, how many (or what proportion) of each.
       (Frequency table)
Graphical summaries of data: Area represents proportion.
     Categorical: Bar or pie graph  (Bar chart ordered by size = "Pareto chart")
             Pie only ok if showing all categories.
What about smoking and brain injury?  What were the merits of each display?

    Quantitative: Histogram, Stemplot (Stem-and-leaf), Dotplot
      (I will only require you to read, not make histograms by hand. You'll Make stemplots and dotplots by hand)
    Will Discuss Friday:   Pretest:  Restate #5 as histogram of 100 "5-volt" batteries tested for actual voltage.
              The proportion with voltage < 1 is 20.  The proportion with voltage < 3 is 60.
               a) What proportion have voltage beween 1 and 3?  b) What proportion have voltage > 3?

 Histogram can change somewhat depending on intervals you choose.
  Moore Applet (
http://bcs.whfreeman.com/bps4e)  . or use disk in book) One Variable Statistical Calculator, text pp. 11-13, Ta 1.1
 
Stemplots (Stem-and-Leaf) are a powerful hand tool. 
Tally, value added.  Handout
            !!Unordered first,!! then ordered if necessary.  By tens, then split?
        Back to back, comparing two groups.   (or side-by-side on same scale, cf. p55 fig. 2.5)
                       Data from class so far

Describing:  Pattern-- and deviations from it
   Shape (symmetric, or skewed (think smeared, or sliding) right or left), (&& bell-curve (Ch 3), J-shaped (fig.1.15a p.31))
        (Humps: uni- or bi- modal (multi-)   Two humps = two "causes"?)
   Center (roughly--half on each side) , Spread (smallest to largest)
   Outliers,  gaps ? (different groups, sources?)dotplot

Dot plot:  Draw a horizontal axis, pile up dots at the appropriate points.   
Note top of p. 49, fig. 2.3, use of a dot plot to display a data set of size n = 7.
Choosing a display (by hand):
    A dot plot is most useful for n = 3 to about 15-20, or when the data only fall on a few values (just stack the dots up).
    A stemplot is good for continuous data, smeared around; you can do 100 values in 3-5 minutes.

What do we see?  What can we infer? (Introduction)
    Data source? Lurking variables?
    Variability happens.  Things settle down on average, BUT conclusions are never certain.
    Statistics gives us a language for talking about uncertainty.


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