Math Forum Discussions

Jeff Holcomb

Posts: 18
Registered: 9/12/05

Standard Deviation and Chi-Squared
Posted: Nov 7, 2011 1:30 PM

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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 Chi-Square 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 Chi-Square.

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 Chi-Square).

Thanks again.