Math 151 , Day 5 Monday, Sept.6, Fall 2004 Hit reload to get most current versionAfter Class

HW Day 5
Reading:   pp.37-40, standard deviation:
PLEASE read ahead in 1.3,  Normal Distributions:  There's a lot there, and I will cover a good chunk  Friday
Hand in
Standard deviation(Lost handout? Link) 
p. 40, 1.34 a. Graph the data with a dotplot.   Use SPSS to  do c.  Write your answers from screen to paper.  Do  b by hand .

1.35 (Maris HRw/w.o.outliers) Graph the ten values with a dotplot.  Use SPSS to do the calculations.  Just delete the outlier and repeat the analysis.

p. 44, 1.42   xbar=7.50, s = 2.03 the same for both dist's. Don't do the calculations--just make stemplots & compare their shapes!
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 Postpone to Friday: Complete Handout on Densities (get from outside my door if you missed class) 

 Read, to discuss 

1.43 states' oldies: which?why? (don't calculate) 
 

 Optional 
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+Next time (Friday) meet in Mac 101. SPSS Bring Text, + a floppy or Zipdisk or RW CD.
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Leftovers: Galton board--balls and pins (bell shaped "normal" distribution)  Many small independent influences.
Other measures of middle exist, tho are less common.  Midrange:  halfway between min and max.  Mode(Modal class): category with the most individuals.  Trimmed mean: Trim (throw away) a small proportion of largest and smallest.
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HW questions?  Highway speed?
Quartiles, five number summary, boxplot, IQR Day 4

SPSS, for simple computation: Handout

Standard deviation (measure of Spread that goes with mean)
            Variance s2:  (almost) average of squared deviations from the mean.
                 (Divide by (n-1) "degrees of freedom")
         s : Standard deviation  is the square root of the variance.
                Computation:  I will require you to know how to do it by hand for 4 or 5 observations
                              (see p. 38 for formula, p.39 for pattern).
             Physics: angular momemtum (spinning ice skater)
             Not so weird: High school geometry?
         Remember Pythagorean theorem: c2 = a2  + b2:
                hypotenuse of right triangle is also square root of a sum of squares.
        Very sensitive to outliers (squared  deviations do it)
     Mean/standard deviation pair useful for symmetric, unimodal (one-humped), no outliers. ("Normal" dist.)
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Spinner. Use 248x310 pixels

Start here Friday:  Density curves, pp.46-51
GET  handout HW sheet: "Density curves"
    (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.

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.
    • 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.

  • You will make and use tables for the simple distributions on the handout.  These are similar to the table we will use to describe the normal distribution.

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