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Standard Deviation and ChiSquared
Posted:
Nov 7, 2011 1:30 PM


Hello oh helpful ones,
Something I am confused about. Consider the following data for flipping a fair coin.
Name...........H........T Alberto........14.......6 Bernard........55......45 Cynthia.......460.....540
The question is, which one is the "weirdest"?
My kids and I figured one way to answer this was to see how many standard deviations from the mean each of these values represent. We had recently conducted a simulation with TinkerPlots where we collected the results of 100 experiment where each experiment consisted of flipping a fair coin (spinner) 50 times. We ended up getting a mean of 25.3 and a standard deviation of 3.2 from our experiment. We scaled these results to match the sample size for Alberto, Bernard, and Cynthia respectively. We then used this results to determine how weird we thought it would be to get the given number of heads (assuming a fair coin). Here are our findings:
Name...........H........T............# of SD from Mean........How Weird Alberto........14.......6..................3.03...........................Very Bernard.......55......45.................0.688.....................Not Weird Cynthia......460.....540...............0.719.....................Not Weird
Then we computed the ChiSquare value and used it to quantify the weirdness.
Name..........H........T..............Chi Square...........How Weird Alberto......14........6.................3.2....................Pretty Weird Bernard......55......45..................1.....................Not Weird Cynthia.....460.....540...............6.4...................Very Weird
It seems to us that we are getting contradictory results. We were expecting that if SD told us the data was weird, then so too would ChiSquare.
What am I missing here? Do you think it is a calculation error or am I missing something vital with these two measures (SD and ChiSquare).
Thanks again.



