01. Invent Yourself: Good Guesses LaplaceWitches Nanjing Foreign Language School 2017.6.29-2017.7.4

2017 IYNT 01. Invent Yourself 01. TOPIC REVIEW 02. THE EXPERIMENT 01-2. KEY WORDS 01-3. OBSERVATION LaplaceWitches 02. THE EXPERIMENT 03. DATA ANALYSIS 04. CONCLUSION 05. FURTHER DISCUSSION

01 TOPIC REVIEW 01-1. TOPIC 01-2. KEY WORDS 01-3. OBSERVATION

TOPIC REVIEW INVENT YOURSELF:GOOD GUESSES In 1906, Francis Galton observed a contest where 800 farmers guessed an animal's weight. To his surprise, the median of the guesses was within 0.8% of the true measured weight. What is the chance of obtaining such a good match by coincidence? Select an interesting and important parameter, measure it directly, and give a group of human observers the task to guess the value of the parameter. Discuss the results of your experiments.

TOPIC REVIEW KEY WORDS KEY WORDS 800 Farmers Median Of The Guesses

TOPIC REVIEW OBSERVATION Regression toward the mean In statistics, regression toward (or to) the mean is the phenomenon that if a variable is extreme on its first measurement, it will tend to be closer to the average on its second measurement—and if it is extreme on its second measurement, it will tend to have been closer to the average on its first. Standard deviation A measure that is used to quantify the amount of variation or dispersion of a set of data values.

02 THE EXPERIMENT

Parameter: the number of candies EXPERIMENT Parameter: the number of candies Samples: 90 students’ guesses

03 DATA ANALYSIS

GRAPHS

GRAPHS

REGRESSION TOWARD THE MEAN

03 CONCLUSION

CONCLUSION From the further illustration of the frequency and normal distribution curve, we can draw the following conclusions: The normal distribution curve is not ideal; Although both the median and the average are 10% lower than the real result, the experiment is very similar to the theory of regression toward the mean. This means that the mean of number of sugars would “regress” all the way back to the original figure. No matter how big the range is, the median number is always close to the right answer. According to the experiment, the job and age of human observers don’t affect the result much.

04 FURTHER DISCUSSION

The samples are probably not enough, and if possible, we can UNCERTAINTY The samples are probably not enough, and if possible, we can Due to the limited observation time slot by each student, some students may not observe the jar completely, thus will affect the estimation of the number of sugars. The shape of the bottle might cause the unnecessary illusion of those human observers. The candies have gaps between them, which might affect the result, too.

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