# Advanced Data Analysis: How Physicists Find a Needle in the Haystack

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Basic Graphing Dynamics - Observe Model Particles - Load Data - Answer Questions
Advanced Data Analysis - Refine Your Information - Cut Data - Extend the Activity
REFERENCES

Warning: You will need Netscape 3.0 to run the JavaScript on these Web pages.
Refine Your Information - Cut Data - Extend the Activity

• Different Plots of Same Data
• Cutting and/or Including Points
• Statistics Revealed in Histograms

## Classroom Use

Given the complicated options on this page, it is best employed by students independently after they have experienced a lesson with the basic histogram pages. The teacher could divide the class into three groups or into three sets of small groups. The goal of each group would be different.

By looking at the year distributions, one group could try to establish at what rate pennies fall out of circulation. Their results would be more accurate if they research and find how many pennies were minted each year. Students might be able to conclude that the approximate proportion of minted pennies "lost" from the money supply each for each minting year follows some kind of exponential function.

By looking at mass distributions, a second group could work on the problem of what metal went into 1943 pennies.

A third group could establish some guidelines for choosing a bin width. Many thin bins can make a set of data look jagged. On the other hand, thick bins can conceal some of the interesting bumps in data. By looking at the mass distributions, this group should relate the range of values (maximum - minimum = range) to the bin number and to the number of data displayed. It will not be a mathematically precise formula, just a rule of thumb that make a smooth histogram likely on the first try.

## What Happens on the "Load Data" Page

Students have greater control over the analysis in these pages. First, the student can load the penny data into the text area. Then the program reads the data to make a control panel. Then the student can adjust the control panel to make a graph.
Students can get a feel for how data analysis is accomplished. Each coin is actually represented by three measurements: its mass, its mint, and its year. Students may put either the mass or the year on the horizontal axis to view its distribution. All three factors may be set with the control panel. Lowering the maximum or raising the minimum will have the effect of removing some of the coins from the final distribution. Similarly, including only one mint instead of two or three will cut down on the amount of data that is graphed.

## Background Information

These pages are very similar to the basic pages. They allows students to analyze the masses of pennies so they can find patterns that suggest how the coins have changed in past decades. They are an improvement over the basic pages in that they come with two sets of data of 250 pennies each. One set contains measurements from pennies that were randomly accumulating in one person's pockets during the autumn of 1997. The other set contains measurements from pennies that were collected and stored in a jar over the years.
Author: Francis Lipinski, 1997-98 Fermilab Teacher Fellow
Web Maintainer: ed-webmaster@fnal.gov
Last Update: June 12, 1998