Math 151 , Spring 2002, Day 6, Friday, Feb. 8 Hit reload to get most current versionUpdated late Sunday:

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HW questions?
Review five number summary, boxplot, IQR
Bimodality of car weight?
Drive ratio: the amount of power your engine puts out to rotate your rear tires one full rotation.(Thank you Nicole M.)

Standard deviation (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. 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.)

Start here Monday:
Changing units:  Not in Moore.
    ( + ) Measures of middle should shift  along with the raw data.  Measures of spread are unaffected by +
    ( x ) Measures of middle and of spread should stretch or shrink along with raw data
                  (We assume we only multiply by positive numbers.)
Alias/alibi:  When you change units of measurement for all your data values, you can think of the result 2 different ways:
    Alias (other name):  The data distribution sits still. You have just changed the ruler stick you measure by.
             (in/cm ruler.  Thermometer)
    Alibi (other place) :  The ruler stick stays the same, and the data distribution with new values moves to the new location.
        Activstats demo shows this (4-4)
We'll change units when we "standardize"--with the normal density.  Moore pp. 55-7

Density curve (1.3) --a mathematical model (abstraction) of a histogram.  (For Quantitative, continuous data)
"x-axis" gives possible values of observations.
Proportion of Area above an interval = proportion of all observations we would find in that interval.

  • Median:  point that cuts area in half.
  • Mean: balance point.

    •           Same patterns as for histogram-data;
                Symmetric: mean=median.  Skewed: Mean is pulled to long-tail side of median.
    HANDOUT on general densities.

    PreClass assignment Day 6 for Day 7
    ACT 5-1 (Densities), 3-4 (Normal Distribution only), 
    5-2 Normal Density (see Teacher Note. I like this method better now, because if you check the Normal box when you make it, the next time you make a histogram the Normal Curve will still be there.  Make the histogram, double-click to get the Edit bars.  Then Format>Graph Elements>Histogram, Check the Normal Curve box.)
    Be ready to answer questions in class on Densities and the Normal Density.

    HW assignment Day 6, Friday, Feb. 8,
    ACT: From Activstats Homework
    Moore:  From David S. Moore, The Basic Practice of Statistics
    Reading: Finish 1.2, to p. 42.  Next, 1.3
    Hand in :
    Moore: p.40, 1.34 a and b only.  Do a dotplot also.*
    p. 44, 1.42 (don't calculate: xbar=7.50, s = 2.03-- the same for both dist's) Do stemplots--compare their shapes!

    (SPSS)ACT HW Ch 4, ACT-1 (Acid Rain).  Besides those questions, make a Time plot.  (Use Case for the x axis.  If you use the Date variable, it will put them in alphabetical order.) 5 is closer to "normal" rainfall than 4.   How does this add to your understanding?

    To be assigned Monday:
    A) The U.S. is almost the only country left that uses Fahrenheit to measure temperatures. To change F to C (Celsius), you subtract 32, and divide by 1.8.   HANDOUT with both scales ("Alias"). 
    a)  The temperature as I write this is 500 F.  Calculate the temperature in C, and mark the temperature on the handout. (Check your calculation on the scale)
    b)  If the mean high temperature in Ithaca during  Feb. is 40o, and the standard deviation is 100 F., and you want those in Celsius instead, what do you do? Calculate  the results.  Check your results with the handout scales.   

    		 Read, be able to discuss 

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

    		 Optional 
     
     

     
    * Answers 5.4, .642.  On a test, I will give only datasets with "easy" differences, max 5 data points

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