We often need to visualize and interpret the distribution of data.

Histograms

Students interpret histograms, the graphical representation of the distribution of data.

They articulate the difference between a histogram and a bar graph: a histogram compares number ranges, such as ages or averages, whereas a bar graph compares categories.

Normal distributions

Students recognize that many phenomena follow a normal distribution, or bell curve, in which the distribution of data points falls around the mean in a predictable pattern.

Furthermore, they recognize that, according to the central limit theorem, the averages of even non-normally distributed phenomena often will have a normal distribution.

Power law distributions

Students recognize that the distribution of many phenomena--such as earthquakes, the population of cities, human performance across a wide variety of activities, and arguably fluctuations in the stock market--follows a power law distribution, or "fat tail" distribution.

The distribution can be seen most clearly when the frequency (the y-axis) is expressed on a logarithmic scale, such as this distribution of earthquake frequencies.  A good model will help us to predict the frequency of extreme events; is a 9.0 earthquake to be expected every 10 years, or every 100 years, or every 1,000 years?

Students express the differences between power law distributions and normal distributions.  In power law distributions, the mean is far lower than the mean in the normal distribution, and extreme phenomena (on both ends) are more common than are predicted in the normal distribution.  The power law distribution even has implications for how we grade students!

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