# Don't Leave Learning to Chance

**Abstract:**This article presents a simple exercise for teaching probability distributions, useful for both new learners and those refreshing their memories. Students are provided with a chart showing the possible totals generated by the throw of two ordinary dice. They are instructed to fill in the possible ways the dice can generate each total, then use this information to calculate and fill in the frequency and probability of each total, the mean, the difference from mean for each total, the variance for each total and the standard deviation. If time permits, the students can be invited to roll a pair of dice and a histogram of an actual distribution of dice rolls can be …

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Excellent article. I don't get why someone would criticize this article. It is a very straight-forward approach to a topic that confounds many. Mr. Howard, thank you.

--Jim Bongard, 02-12-2011

Really well-thought-out exercise. I feel bad that most of the Six Sigma Black Belts are too dependent on Minitab and not aware of the basics.

--Parag Pradhan, 02-09-2011

This is a fine illustration to teach beginners a very easy concept to grasp. Thanks. More articles like this should be published.

--M.Devidasan, 02-08-2011

An excellent example of a clear lesson on a tricky subject.

--Carlo Enrico Rossi, 02-07-2011

Why, oh, why do we continue to teach stuff like this to college students when the real goal is to get them to THINK "statistically," i.e., handle everyday variation (i.e., treating ANY deviation from a goal as "special cause"). I used to think teaching stuff like this was useful, too (and I got reviews...but so what?). The more I learned about Deming, and the more I understood improvement and his message, the more I realized this is the wrong stuff to teach. We've got to stop this "legalized torture" that people endure to get their "belt" or whatever--Trust me, they don't subsequently use it...or use it BADLY. A GREAT exercise for high school students, though.

Davis Balestracci (former Chair, Statistics Division -- and most of my colleagues probably wouldn't agree with me)

--Davis Balestracci, 02-07-2011

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Well thought out. Good practice example.

--Marilyn Wightman, 05-19-2011