# Class activities/experiments to teach statistical concepts?

I intend to give a one hour lecture to teenagers about statistics. I will probably see them only once. This scenario might happen over and over.

I would like to give them some activity to make them experience statistics. But I am forced to do it with people who do not know anything about probability, statistical inference, exploratory analysis etc.

My thought was to go through some simple visualization "tricks" that the media sometimes uses, and debunk that a bit. (please do not give me a link to "how to lie with statistics" :) )

The other idea is to (also) give them an assignment for running an experiment to discover something. For example: discovering if they can detect the difference between coca cola and RC cola.

I am looking for any suggestions for what to do with them, or resources with relevant materials.

Thanks :)

(of course, making this a community wiki will be nice)

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CAUSEweb has a bunch of good general teaching resources and activities, perhaps there'd be something appropriate for this situation there: causeweb.org/resources –  Aaron Apr 27 '12 at 13:30
In addition to CauseWeb, which is a great resource, check out the (free online) Journal of Statistical Education. –  whuber Apr 27 '12 at 14:50
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## 3 Answers

One thing I have done with students that went over well was to take several packages (the small ones) of M and M's candy and have the students count how many of each color there is in a pack (depending on the number of students they may each get their own or work in groups of 2 or 3). The students can usually figure an appropriate way to dispose of the candies afterwards. If you want more data, or comparisons, or just the "Population Proportions" I have recorded some values here (if you do this consider submitting your data to add).

Then you can use the data that they have just collected to show some basic concepts like variation (they did not all get the same counts/proportions). You can show some basic graphics like a histogram of the proportion of Blue candies, or boxplots comparing the proportions of a color from different types.

I then usually show them the true proportion for one of the colors and show how their proportions, while not exactly the truth, tend to cluster around the true value. I then show how close they tend to be to the truth (a general rule of thumb says that for a sample size of 50 the 95% margin of error will be about 14-15%). Then I show them the proportion of a different color from one of their samples and ask what values of the "truth" would be believable (using the 14-15% rule of thumb again) without telling them what the truth is. This gives a general idea of the concept of a confidence interval.

Another option is living graphs, have each of the students know some numeric fact about themselves (height in inches/cm works well). Clear a space on the floor and put some masking tape down with values written on it (like the axis of a plot). Have the students line up next to their value. You can then climb up on a desk/ladder and take a picture of the living histogram (I have seen this done outside with a tall ladder for a really good effect). Then you can have them count off from each end and put down a stripe of tape where they meet in the middle (the median), then do the same for each half and put down tape for the quartiles, wrap the tape around the middle half, then have them lower that to the floor, add the wiskers and have them step away to see the boxplot remaining on the floor. If there are enough students you could have them do this separately for boys and girls and compare the boxplots.

An activity to show the need to take good samples and avoid biased sampling can be done by getting some regular drinking straws and cutting them to lengths of 1 inch, 2 inches, and 4 inches. Put 4 of each length in a paper bag. Give a paper bag to each group of students and have them take a sample of size 4 from each bag by reaching into the bag without looking and taking out 4 at random. Have each group put their straws back and take a few more samples. Record the means of their samples and create a histogram, show the real mean on the graph to show how their means tend to be larger on average than the truth due to the biased sampling.

You could also discuss some of the principles of study design by having the students make paper helicopters (you can google for templates) and vary some options (wing length, body width, paper clip or no paper clip, etc.) to see if they can find the design that takes the longest to fall a set distance. You can discuss replication, randomization of testing order (what if the wind changes during the testing period?) and other concepts.

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Hi Greg, this is a wonderful list of activities, thank you. By the way, the last one (the helicopter experiment) was used in the first class I took (in the University, several good years ago) in the course "design of experiments and ANOVA". I remember it as one of my earliest "fun" experiences with statistics. –  Tal Galili Apr 27 '12 at 19:38
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Have you seen http://www.stat.columbia.edu/~gelman/bag-of-tricks/?

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Yep, I got it from my library once but had to return it before I got a chance to read it. I will give it a look again, thanks. –  Tal Galili Apr 27 '12 at 20:57
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This is very open ended!

High school level statistics:

If you are a R enthusiast, check out the "TeachingDemo" library it has crazy good 3d simulations!

Get them to gamble (with, say candy) and show them how to increase their odds on: -different dice rolls games -on roulette -card picking

Famous problems you can have fun working through (ie. get them to play the actual games) - Chevalier de Méré problem (ie. the invention of probability theory) - Monty Hall game (Let make a deal) (ie. intro to conditional probability) http://www.mytechinterviews.com/tag/probability (includes google interview challenges)

Videos mostly to hype statistics: http://www.ted.com/talks/lang/en/arthur_benjamin_s_formula_for_changing_math_education.html http://www.ted.com/talks/lang/en/peter_donnelly_shows_how_stats_fool_juries.html http://www.ted.com/talks/hans_rosling_shows_the_best_stats_you_ve_ever_seen.html

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Hi Etienne. I love the teachingDemo, I will give it a look for the 3d simulation (are you talking about the dice role, or are there new stuff I do not know about?). In general, the problem with going R on them (although I LOVE R), is that I will probably not have enough time for almost anything. The idea is to get a "first impression" type class. (for my regular teachings I would use R to teach concepts etc.) –  Tal Galili Apr 27 '12 at 20:59
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