Math 151 , Day 6 Fri. Feb. 8, '08just before class.After class. Hit reload to get most current version

HW Day 6:   Reading:  Ch.2 pp.47-50- standard deviation, Check 2.19, 20, 21, 22:
In Ch.3,  64-9 density curves, & ahead Normal Distributions 70-84: 
Hand in:

Standard deviation
B.  Find the mean and standard deviation of these 4 numbers: 2, 2, 4, 8 by hand.
p. 50, 2.9 Blood phosphate Do a and b by hand.  Use SPSS (preferably)or some other tool** to  do c.  Write your answers from screen to paper.  Also (re)make a dotplot of the data, mark the mean with a wedge, and indicate the standard deviation s with <----> lines from the mean to both sides, s long. (like the sketch Notes, Day 5)

p. 51, 2.10   xbar=7.50, s = 2.03 the same for both dist's. Don't do the calculations--just make stemplots & compare their shapes!
ALSO, type the data for Dataset B into SPSS or other**, excluding the outlier of 12.50.  Find and write down the mean and s.d. now.  Compare to xbar=7.50, s = 2.03 .

Already done:
p.55, 2.12 Rainforest logging.  Use the 4-step process, see below, p. 53-5&/or inside front cover.  Note that "state",  the first step, is usually "done"=the textbook statement of the problem.  The data are probably suitable for mean& standard deviation, but we don't have the SPSS power to do them easily yet, so use your hand methods--stemplots, quartiles, boxplots...  This is one where working together with others can have real benefits, since it's pretty open-ended.
- - -Postpone the rest:  will not be on Exam 1 - - - - - - - 
Complete the Densities Handout  (Link, or get from outside my door if you missed class) Solutions
p. 66, 3.1 Sketch density curves
p. 69, 3.2 & 3.3Uniform distribution This is the same density as A on the Handout on Densities.
p. 69 3.4 means and medians

 Read, to discuss 


Optional

p. 62, 2.40, 2.43  Play with  summary numbers. Use the Applet, One variable statistical calculator; type data in at the Data tab.

More s.d.-by- hand practice:  Find the s.d. of  5,6,7,9,13.  (hint: the mean is a whole number.)

**Where it says to use  SPSS, you may use SPSS (preferred) (Didn't get handout? Link), or a statistical calculator if you have one, or the Applet, One Variable Statistical Calculator, on the web http://bcs.whfreeman.com/bps4e or on the CD in your book.
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First hourly exam  Friday Feb 15 .
Sample exam will be handed out TODAY Problem 7 (density curve) will not be on your exam 1; solutions will be linked here, probably Sunday, paper copy to read outside my door  Monday.  Closed book, but bring one sheet of notes (anything you like) and a calculator.
Exam will cover thru what is assigned Today in Chapter 3.  You may be asked to read SPSS output (as we see it Monday), but not how to produce it.
You may  start early and/or stay late, if you don't have another class.  You don't have to work in the classroom;  you just have to sign in and say where you'll go (in the building!), on the clipboard.  If you want more than an hour, and have obligations before and after--or other problems-- see or email me to make a plan before Wednesday! 
      Wednesday: bring questions. 

New clinic time for Matthew: M 1:30-3:30, F 2:30-4:30
Mallory still: Wed. 7-9 pm, Thurs. 6-9 pm

+Next time (Monday) meet in Mac 101. SPSS! Bring Text, + whatever you store files on.  If you can, and want to, start early, come anytime after 10:30.
Handouts today: (last time) SPSS--Mean and SD,( New:Tables for Simple Models (Densities))
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Quartiles, five number summary, boxplot, IQR   
HW Questions? A. cars down the highway? Day 4

Summaries of Middle & Spread continued--"Systems:"
-- (Midrange, Range  Very sensitive to outliers--they use only the max and min!)
-- Median, IQR  (+ Quartiles Q1, Q3, 5-number summary), based on percentiles (j'th percentile is > j% of the data)
-- Mean, StandardDeviation "y-bar" (or "x-bar"), "s"  (good for symmetric unimodal, no outliers)

Standard deviation (measure of Spread that goes with mean)  See Day 5 for notes  


Exam 1 covers to here, + reading SPSS output.  Start here Wed.
Ch. 3, Density curves, BPS4e pp.64-69
GET  handout HW sheet: "Tables for Simple Models (Densities)"     Handout )

Spinner. Use 248x310 pixels    (When values can take on any of a continuous interval of numbers)
Example:  Spinner:  Label edge with continuous values from 0 to 1. Spinning should produce 1/10 of all spins in each colored sector.  Simulations of 500, 3000 spins show roughly true. More spins would get closer.
(Histograms of simulations)

Abstraction, idealized histogram ("Mathematical model") = Density curve. Describes a theoretical distribution of data.

Any density curve:  is a curve
   --always on or above the horizontal axis
   --has area exactly 1 underneath it.
Many, many density curves are possible, modeling many phenomena.
  • For the spinner, the density curve is "Uniform on 0 to 1".
  • If you have two spinners like this, spin both at once and add the results--the corresponding density curve is "triangular, symmetric, on 0 to 2"
  • A more complicated mechanism will produce data corresponding to the density curve I have called "trapezoid, -1 to 2"
  • A very important one is the "normal" distribution family (familiar "bell-curve").
    • Median, mean, percentiles, standard deviation are defined for a density curve in analogy to those for a histogram.
    -- median has half of area below and half above.
    -- mean is balance point.  On the long-tail side of median if distribution is skewed. Same as median if symmetric.
    --First quartile has 1/4 of area below, 3/4 above. Etc. for others.

    Many densities have tables to describe them.  Especially tables showing area to the left of (below) a given value ("Cumulative Proportion").

    You will make and use "Cumulative Proportion"  tables for the simple distributions on the handout.  These are similar to the table we will use to describe the Normal distribution.
    Next: Normal density, and Normal table.
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