andrew_gelman_stats andrew_gelman_stats-2014 andrew_gelman_stats-2014-2257 knowledge-graph by maker-knowledge-mining
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Introduction: From 2008: The candy weighing demonstration, or, the unwisdom of crowds My favorite statistics demonstration is the one with the bag of candies. I’ve elaborated upon it since including it in the Teaching Statistics book and I thought these tips might be useful to some of you. Preparation Buy 100 candies of different sizes and shapes and put them in a bag (the plastic bag from the store is fine). Get something like 20 large full-sized candy bars, 20 or 30 little things like mini Snickers bars and mini Peppermint Patties. And then 50 or 60 really little things like tiny Tootsie Rolls, lollipops, and individually-wrapped Life Savers. Count and make sure it’s exactly 100. You also need a digital kitchen scale that reads out in grams. Also bring a sealed envelope inside of which is a note (details below). When you get into the room, unobtrusively put the note somewhere, for example between two books on a shelf or behind a window shade. Setup Hold up the back of cand
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1 From 2008: The candy weighing demonstration, or, the unwisdom of crowds My favorite statistics demonstration is the one with the bag of candies. [sent-1, score-0.674]
2 Preparation Buy 100 candies of different sizes and shapes and put them in a bag (the plastic bag from the store is fine). [sent-3, score-1.621]
3 Get something like 20 large full-sized candy bars, 20 or 30 little things like mini Snickers bars and mini Peppermint Patties. [sent-4, score-0.465]
4 You also need a digital kitchen scale that reads out in grams. [sent-7, score-0.188]
5 Also bring a sealed envelope inside of which is a note (details below). [sent-8, score-0.221]
6 Setup Hold up the back of candy and the scale and write the following on the board: Each pair of students should: 1. [sent-10, score-0.578]
7 Silently multiply the weight of the 5 candies by 20. [sent-18, score-0.834]
8 Explain that their goal is to estimate the total weight of all the candies in the bag. [sent-22, score-0.834]
9 They can choose their 5 candies using any method–systematic sampling, random sampling, whatever. [sent-23, score-0.774]
10 Demonstrate how to zero the scale, give the scale and the bag of candies to a pair of students in the front row, and let them go. [sent-26, score-1.528]
11 Take a look to make sure the scale and bag are moving slowly through the room. [sent-29, score-0.517]
12 Now call up two students from the class (but not from the same pair) to look at all the estimates. [sent-37, score-0.24]
13 Now give the bag to the two students in the front of the room and have them weigh it. [sent-40, score-0.71]
14 Punch line The weight of all 100 candies will be something like 1658. [sent-41, score-0.834]
15 Write this true weight as a vertical bar on the histogram that you’ve drawn. [sent-43, score-0.21]
16 Now call out to the students who are sitting near where you hid the envelope: “Um, uh, what’s that over there . [sent-45, score-0.234]
17 ” A student opens it and reads out what’s written on the sheet inside: “Your guesses are all too high! [sent-54, score-0.226]
18 Large candies are easy to see and to grab, while small candies fall through the gaps between the large ones and end up at the bottom of the bag. [sent-56, score-1.515]
19 It won’t be obvious to the students that the way to do a random sample is to number each of the candies from 1 to 100 and pick numbers at random. [sent-59, score-0.955]
20 Remember–it’s crucial that the candies in the bag be of varying sizes, with a few big ones and lots of little ones! [sent-67, score-1.205]
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