Sunday, September 20, 2009

Scatter Plots and Souffles

Most people freeze up at the sound of algebra, or anything hard having to do with numbers.
Why is that so? We can use this information to do tons and tons of things in real life, for fun, for work, and for efficiency. Like scatter plots.
I don't mean to sound too preachy about how great math is, since I used to be one of the naive, but data's a pretty interesting concept. If it looks like just a bunch of crazy calculator button pushes and some dots on a graph, apply it to something cool, like volcanoes, or souffles. With a different frame of mind, graphs can be easy, and lots of fun!
So. Scatter plots.
Scatter plots basically show the correlation between a bunch of different points on a graph. These points show data. A line can be drawn through the graph to show whether or not the points even have correlation, and if they're positive or negative. Simple, right?
In order to draw a scatter plot on your handy-dandy calculator, there are some steps you have to follow.
Let's make our own scatter plot. Back to souffles. Say you want to make some souffles. You don't know what temperature you want to bake your souffle for. At different temperatures, souffles rise and fall. If we put in a pan of 12 souffles for thirty minutes six times, at six different temperatures, what would the souffles' heights be at 400 degrees?
We can determine this by using a scatter plot.
Hit "STAT" on your calculator, then select 1. Edit, and hit "ENTER." Put in your six cooking temperatures into L1, the independent variable, and the height of each of the souffles on each tray into L2, the dependent variable.
Then, hit "Y=" and highlight "PLOT 1" at the top of the screen. Clear anything already in "Y1"
Hit "ZOOM" and select 9. ZoomStat, and hit "ENTER." This should plot all of the points from your experiment, with the temperatures as X, and the souffle heights as Y.
To complete your scatter plot,
Hit "STAT" and select Cal 4: Lin Reg (ax + b). Sound familiar? This gives you your rise over run, mx +b. Your calculator just calls it something else.
Once you have LinReg (ax+b), hit "2nd" and "1" for L1, "2nd" and "2" for L2, and "VARS", "Y Vars", 1: Function, and "ENTER" for Y1. Put a comma in between each one.
Your calculator should read: LinReg (ax+b), L1, L2, Y1.
Hit "ENTER."
Here's all your information. Go to "Y=" for your Y-intercept and line equation.
Check that your L1 goes all the way up to 400 degrees. You can check your table by going "2ND", "WINDOW." Set TblStart to 400. Then, go to "2ND", "GRAPH", which will bring you to "TABLE." Here, you can see what the souffle height would be at 400 degrees in L2.
Now, hit "GRAPH". There's your line and correlation!
Write down all of your data. There you go!
...And you thought souffles and scatter plots had nothing to do with eachother.

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