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Topic: log paper and hand calc and Reese's
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Posts: 132
Registered: 12/6/04
log paper and hand calc and Reese's
Posted: Jun 10, 1996 10:57 PM
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I sent my two cents before I read all my incoming mail. Now youall will have
to be patient with this old physicist while she answers the mail.
As a rite of passage to the appreciation of calculators and KaleidaGraph
on the Mac, I instruct my kids in the art of the hand calculation of standard
deviation, the linear regression eqn and the correlation coef. (Which I
taught with grave seriousness 15 years ago and used in research 30 years
ago). With a set of collected data, they compare their hand calc with the
calculator and with the computer. They see the factors involved and the
relationships of the factors. Done once is enough.
On exponentials, we use kid collected data (say radioactivity or
Newton's law of cooling) and graph on semilog paper first -> go to
Kaleidagraph (plots loglog and semilogs). For loglog plots, we do Kepler's
law concerning period vs ave distance from sun. One is power of 2 and the
other power of 3, hence log log to straighten out.
About the cubic and quartic and higher powers of poly. One can fit
anything to a high power -> and it is meaningless. This is the time for the
lesson in meaning of eqn vs best fit. They must find a resource or think
about physics and extrapolated values. A good one is the stopping distance
of cars at various speeds (data from Georgia Drivers Manual (which they all
have)). Fit to quadratic or cubic and the extrapolated distance for 100 mph
is outrageous. Point made.
Another outrageous extrap is from cumulated number of cases of AIDS
diagnosed (downloaded from CDC webpage) . The last year shows a tad of a
decrease and decrease is predicted for the future. (It is being modelled via
diff eqs.; my class attended a lecture by a man currently doing this). On
the reverse is TB, which was exponential decay until 1988 then the graph
turns up (data from CDC by phone).
The value is in the discussions of fit or not and why. Not the
transformations to linear - though some of this math is important,too. In
fact, I will start doing that next year - on yourall's advice.
Rex - Reese's pieces are like M&Ms except peanut butter in the center
instead of chocolate. Hope you have M&Ms over and under there. Reese's come
in three colors while M&Ms in six (I think). All with different %
Now back to grading finals - and eating M&Ms.
Alice, Galloway School, Atlanta

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