Modification

Modification

toc



Introduction
Modification is quite an easy task to accomplish when using Fathom. Fathom provides users with several built-in functions that allow for significant task design when using data and can be used in both a statistics and probability setting. The following activity will provide a statistics lesson. I will attach another file, however, that can be used in a probability lesson. Be creative when thinking about modification and how a probability task fits in. Modeling is achieved very easily at the modification level. This activity allows students to apply modeling.

File
The first file, "modification.ftm" is the file that we will be using to execute the activity below. The second file, "modification2.ftm" is the probability discussed in the introduction.





 Note: You'll need either the Fathom disc or the free trial of Fathom in order to complete this activity. Click [|here] to download the free trial.

Activity
This investigation requires students to pull real-world data crime statistics data from the Internet and work with a statistical model that can help answer a question. The data has been collected from 1988 to 2006 from crime reports posted by the FBI. The data is collected and grouped into several different variables. Have students use this data, as well as use the internet, to predict how many new jails need to be constructed or how much more hired law enforcement is needed in the United States.

 Crime rates are sprouting up all across the United States. With an ever-growing population, the variety and frequency of crimes are ever-changing. Students need to consider all crimes and come up with reasons as to why there is a flux in these crimes. Are there any correlations? Have students examine data and design their own jail regulations and develop how long a crime puts someone in jail for. This modeling activity will have students look up data and use their interpretive models to construct their own jails. What factors must be considered.

Questions to Think About (Modeling)
- Can you use these data to predict the future crime rates? - Do you think that there will be a time that crime will drop? When? - Is there a correspondence between any two crimes? What reasons can you come up with for this? <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 120%;">- How many new jails will we have to make for specific criminals based on the data you have analyzed?

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 120%;">Using Fathom to do this:
<span style="display: block; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 120%; text-align: left;">1. Visit the following website: [] <span style="display: block; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 120%; text-align: left;">2. Click on the 2007 data collection <span style="display: block; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 120%; text-align: left;">3. Under the "Offenses Known to Law Enforcement" tab, select the link that reads "Go to Offense Table" <span style="display: block; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 120%; text-align: left;">4. On the right-hand side of screen, go to the tab that says "Data Tables" and select "Table 1" <span style="display: block; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 120%; text-align: left;">5. Once it brings you to the table, go to File, Save As. <span style="display: block; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 120%; text-align: left;">6. Name your table "CrimeRates.html"

<span style="display: block; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 120%; text-align: left;"> Note: You must have the .html extension to import the table into Fathom

<span style="display: block; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 120%; text-align: left;">7. Open Fathom <span style="display: block; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 120%; text-align: left;">8. Under the "File" drop-down menu, select "Import" then "Import from File" <span style="display: block; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 120%; text-align: left;">9. Locate the file you saved as "CrimeRates.html" <span style="display: block; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 120%; text-align: left;">10. A new collection appear in your Fathom document.

<span style="display: block; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 120%; text-align: left;"> Note : This part has already been done for you in the above file. This demonstrates how the modification step is satisfied.

<span style="display: block; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 120%; text-align: left;">11. Open the Inspector. <span style="display: block; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 120%; text-align: left;">12. Drag down a graph. Drag the attribute "year" and place on the x-axis. Drag the attribute "Robbery" on the y-axis. <span style="display: block; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 120%; text-align: left;">13. What's wrong with this?! <span style="display: block; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 120%; text-align: left;">14. Right-Click on the graph and scroll down until you see the option "Rescale Axes". Then, click on the x-axis named "Year". This should bring up a window that allows you to edit or adjust the x-axis. <span style="display: block; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 120%; text-align: left;">15. Discuss with students what the x-axis should read. Change the xLower and the xUpper to fall between the years 1980 to 2020.

<span style="display: block; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 120%; text-align: left;">Click here to see the progress so far. <span style="display: block; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 120%; text-align: left;">16. Have students explain how this changes how they can interpret the data.17. Have students drop different attributes on the y-axis and create regression lines. Have them record their algebraic equations and the correlation coefficients.18. Have students also record their data on sheets like this:

<span style="display: block; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 120%; text-align: left;">17. Next, have students examine the following pdf file to determine or get ideas for regulations for jails:

<span style="display: block; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 120%; text-align: left;">18. Have students plan a proposal for expected number of jails (or, if you really want to challenge them have them create their own algebraic expression for the growth of number of jails) by using their Least Squares Lines and their correlation coefficients as justification.

<span style="display: block; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 120%; text-align: left;">Why is this Modification:
<span style="display: block; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 120%; text-align: left;">- We imported a HUGE data set <span style="display: block; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 120%; text-align: left;">- We were able to check several variables and look for several correlations <span style="display: block; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 120%; text-align: left;">- We were able to compare several data sets at once <span style="display: block; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 120%; text-align: left;">- We were able to use real-life data to project the number of jail increases <span style="display: block; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 120%; text-align: left;">- This isn't something that we'd be able to do on a graphing calculator.