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Welcome to Dijemeric Visualizations

Where photography and mathematics intersect with some photography, some math, some math of photography, and an occasional tutorial.

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Tuesday, March 23, 2010

Twenty Random Points Resolved

What is Random?
Random to many means 'chaotic and without structure' but random has pattern, predictability, and order. Flip a coin 100 times. Before you do that, see if you can predict the number of heads. You will probably predict 50 and it may or may not be correct. You should be close, however. How close? That's a matter of statistics and why I say random events are ordered events and are predictable. I would predict on a toss of an unbiased coin, one you haven't shaved or weighted, that it will come up heads 40 to 60 times and if you were to repeat the 100 tosses 1000 times, more than 90% of the tosses would be 40 to 60 heads.

A Real World Example
Another example. You run a wastewater plant. It's regulated on the amount of lead you can discharge. Over the last year you have collected 20 data points for your lead discharge with an average of 20 ug/L with values, a high of 48, and a low of 15. The standard deviation (a measure of the spread of the data) is 10 ug/L. Your manager is concerned and asks 'what are the odds we will have a violation next year'. His concern is real as you regulated limit is 35 ug/L and 30 ug/L is getting close.

In the upper chart, the data are plotted in a time series from the first collected sample to the last. It looks pretty chaotic to me.   When the data are sorted as in the plot above they appear to be nicely distributed around a defined center (average) with a predictable scatter.   Data can be meaningless noise or significant information depending on how they are organized and presented.

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