|Module 3 - Logistic Growth|
|Introduction | Lesson 1 | Lesson 2 | Lesson 3 | Self-Test|
|Lesson 3.1: Scatter Plots|
In this lesson the spread of a disease will be explored by looking at a simulated experiment that was conducted by a class of 25 students using the
The premise of the experiment is that an initial person gets a disease on the first day and infects another person on the second day. The two people who have the disease each infect another person on the third day. The process is repeated daily until all the people in the class have the disease. The number of people who have the disease is noted each day and recorded. It is okay for the people chosen to be infected in a given day not be newly infected.
A Model to Describe the Growth of a Disease (or a Rumor)
Students in the experiment were numbered 1 through 25. The students then entered their assigned number into their calculator's
If this is the first time you have opened the Stats/List Editor since you turned on your calculator, you will see the following dialog box.
This dialog box can be used to create a separate folder for statistics applications, but you don't need to do that for this activity.
If you want to repeat the experiment do NOT reset the random seed values in the student calculators as done initially. Repeating that process will produce exactly the same results.
Random Integer Generator Feature
To begin the experiment the teacher randomly chose a student who would initially have the disease by using the command TIStat.randInt(1,25), which generates a random integer between 1 and 25. Click here to see keystroke instructions to enter the random integer command.
Generating the Experimental Data
The initial student then chose another person at random with the command TIStat.randInt(1,25). This made two infected people at the end of the second day unless the infected person chooses their own number. In this case there is only one infected person on day 2. On the third day, the two infected people choose two more people at random by using the same command. The selected students may or may not have already had the disease, and if a student that had already been infected was repeated, the student who generated the repeated value did not generate a new value. On subsequent days, each of the people infected then chose another person at random. Each day the total number of infected people was recorded. This process continued until everyone had been infected. The table below is a record of the number of people that had been infected.
Displaying the Stats/List Editor
Before you can enter this data into your calculator, you must display the Stats/List Editor.
The Stats/List Editor
The screen below is called the Stats/List Editor.
Values for the Days
As you enter a value, it should appear in the Edit Line at the bottom of the screen. When you press the value should appear in the list. If you enter an incorrect value into the list, position the cursor at that value and simply enter the correct value. You can insert an entry in the list with [INS] or delete an entry with the key.
Data for the Number of Infected People
List1 and list2 should contain the data.
Create a Scatter Plot
Now make a scatter plot of the data.
If "Plot Type" does not indicate "Scatter,"
If "Mark" does not indicate "Box,"
Define the Lists that Contain the Variables
The Define Plot 1 dialog box should have the selections shown.
Create the Scatter Plot
This shape is called a logistic curve.
3.1.1 What are the window values for the scatter plot shown above? Click here for the answer.
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