Math 151 , Spring 2001, Day 3, Friday Feb. 2  Hit reload to get most current version

proposed..
HW:  Our grader/assistant is Mary West.  She will mostly be able to return HW the class day after it's turned in. If there are parts you would especially like feedback on, mark them.
Lateness policy:  If HW gets into the yellow folder (left outside my door after class) befor Mary picks it up and grades it, it's not late. Late HW's will be marked "Late" and not read.  But Late is better than never, for your record.

Old HW
  Bar graph (categorical) should have spaces between the bars, showing we have separate categories.
  Histogram (quantitative) should not, usually, showing that values could be anywhere on a continuous line.
    (The only possible exception: possible values are a small number of small whole numbers, like number of siblings.)
  Stemplot: truncate or round? See Day 2HW

Dot plot.  Day 2

Time plot.  Watch out for extrapolation.  Trend, cyclic.
    Research data: time, or order of taking measurements, is often a lurking variable.  Always do a time plot.

Section 1.2:  Summarizing distribution info with numbers
Measures of middle (central tendency)
    Mean (common "average"):  Take sum (aggregate) of all observations and divide by how many (n)
        Metaphors.  1) Center of gravity, balance point of histogram.
                2) Slice off bits from the big and add to the little till everyone has the same.
        Outlier or long tail will pull mean in that direction (think seesaw balancing)  "Sensitive" to outliers, skewness.
        Especially useful: 1) For symmetric, tidy distributions
            2) When metaphor 2 makes sense--looking for "fair share" of a total.
    Median: half are bigger, half are smaller
        Point on histogram with half the area to the left, half to the right.
        Calculating:  Put observations in numerical order (stemplot!).
                            Middle one if n is odd, or average the 2 middle  if n is even.
                Formula:  Count in how far?  (n+1)/2 places.  (7 1/2 places? go halfway =average the 7th and 8th observations)
        "Resistant to skewness and outliers"--trimming off ends will make little difference in median value.
        More "typical" than mean, if there is skewness or outliers.
    Symmetric distribution: mean = median

Measures of Spread (dispersion, variability)
    Range:  largest - smallest.   Resistant?  NO!  Two observations carry all the info; the rest could be anywhere.
Dot plots of 3 distributions, all with same range:
.       .
.       .
.       .
.       .
__________
                                   We need measures of spread that will better take into account  all the observations: (next)
.........
__________
                 Quartiles, five-number summaries, boxplot, InterQuartile Range.
    ..
    ..
.   ..  .
__________
                                    Variance, Standard deviation.


HW assignment  Day3, Fri. Feb. 2,
From David S. Moore, The Basic Practice of Statistics, unless otherwise noted.
Reading:   rest of 1.1, 1.2: to p. 32 for this hw.
For lecture day 4:  5-number summary and boxplots,to p. 37,
        +  annotated 5-number summary page handout (handed out day 3),
        +   ( standard deviation & summary), p. 37- 42.
Do the means and medians required here by hand (with a calculator).  Make the timeplot(s) by hand.
Hand in 
p. 19 1.10 (time: trend&cycles)
Make a timeplot of McGuire's HR's (data p. 28, or p.23, 1.19)  Any trend? 

p. 32 1.28 (C-sec. mean and med.)
   1.29 (rich: mean or med?)
p. 45, 1.48 (mean or median?)
 

 Read, to discuss
p. 69 1.74 (hospital discharges)
 
 

p.45, 1.46 (net worth) &47 (athletes)
 

 Optional 
p. 22ff, 1.21 (time: flu-lag)
Sievers home  Math151-Sp01/Day3.htm  3:30p 1/31/01
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