Data Matters with Fathom! Dynamic Statistics™ software

Activity 1.2

The project in Section 1.2 requires these four steps.

1. Use the random number generator to create random observations. When you are done, each cell will have a single number produced by the random number generator.
2. Look at the first 20 random numbers. There should be no sequences in them that you can see. Most random number generators have a way to produce random decimals between 0 and 1, for which every decimal is equally likely and shows up an equal number of times. Figure out how to get this kind of random number in your software.
3. Repeat these steps to see how the random number generator produces new random numbers.
4. Figure out what the chances are that the random number generator will produce a number less than .5. (This may be tough, and I strongly recommend you ask friends for help in thinking this through.) Write down your answer and how you figured it out.

Here is how to do each step.

Step 1: Use the random number generator to create random observations. When you are done, each cell will have a single number produced by the random number generator.

Once you are in Fathom, drag a new case table onto the workspace.

Click on <new> to give a name to your column of random numbers. (“RandomNumbers” will work.)

Right-click on the column’s name. Select New Cases. Type in a number. Let’s start with something that’s easy to think about: 3.

Right-click on the column’s name again and select Edit Formula. Type random( . Fathom will write the closing parenthesis in for you.

Click OK.

Add another 17 cases by right-clicking and selecting New Cases again.

Step 2: Look at the first 20 random numbers. There should be no sequences in them that you can see. Most random number generators have a way to produce random decimals between 0 and 1 in which every decimal is equally likely and shows up an equal number of times. Figure out how to get this kind of random number in your software.

random( ) produces random decimals that range from 0 to 1.

Step 3: Repeat these steps to see how the random number generator produces new random numbers.

To create new random numbers, simply hold down “Ctrl” and press “Y.”

Step 4: Figure out what the chances are that the random number generator will produce a number less than .5. (This may be tough, and I strongly recommend you ask friends for help in thinking this through.) Write down your answer and how you figured it out.

This might help: Create a new attribute by clicking on <new> again. Right-click the variable to edit its formula. In the formula window, type randomNumbers < .5 (or whatever you named your random numbers), then < .5 . This will fill your new attributes with True and False. Look carefully, and you will see that there is a True next to each of the random numbers that is less than .5 and a False next to each that is greater than .5.

Get the proportions for this new variable that you just created. (You saw in Section 1.1 how to do this.)

When you use random(), every decimal from 0 to 1 is equally likely.

It might help to have more observations. Right-click on either attribute name and add new cases (you can add as many as 1,000 cases at a time). Look at how the additional cases affect the proportion.

Use “Ctrl-Y” to see the proportions in new sets of random numbers.