## Random Drawing Tool - Sampling Distribution

3-5, 6-8, 9-12
Standards:
Math Content:
Data Analysis and Probability

Similar to the Random Drawing Tool (Individual Trials), this tool generates a sampling distribution by generating a large number of trials. You can choose the type of trial, how many tickets to draw, and how many times to repeat the trial. The results are shown in a histogram and table.

Begin by choosing the type of sample you would like to draw at the top of the tool.

• Numbers: This will draw tickets from a set of numbers you specify and record the numbers drawn.

To use the numbers sample, click on the numbers to the left. They will be added to the sample box. You can repeat a number however many times you like. To delete a ticket from the sample, click the number in the sample box. A maximum of 21 tickets can be added to the box.

• Dice: This will roll 1, 2, or 3 dice at a time and record the sum of the dice.

To use the dice sample, choose the number of dice you would like to throw to the left of the sample box.

• Coin: This will toss a single coin and record 0 for heads and 1 for tails.

The number of Draws indicates how many samples will be taken from the sample box each time. You can choose up to 100 draws. The number of Replications indicates how many draws will be taken. You can choose up to 5,000 replications. (Note: The higher you set these values, the longer it will take to run the simulation.) For instance, if simulating choosing Numbers with Draws = 20 and Replications = 10, then 20 tickets will be drawn 10 times.

Press Start to run the simulation. The results will be displayed below in a histogram and table. Mouse over the bars in the histogram to see the average and percentage for that draw. You can also scroll through the table to see the result of every draw.

Run the simulation listed below. For each simulation, describe in words what the histogram looks like and any interesting features, such as spikes and gaps.

 Type of Sample Sample Draws Replications Numbers 0, 1, 2, 3, 4, 5 5 50 Numbers 0, 1, 1, 1, 1, 2, 3, 4, 5 5 50 Numbers 0, 1, 2, 3, 4, 5 5 100 Numbers 0, 1, 2, 3, 4, 5 50 50 Dice 1 Die 5 50 Dice 2 Dice 5 50 Dice 3 Dice 5 50 Dice 2 Dice 5 100 Dice 2 Dice 50 50 Coin n/a 5 50 Coin n/a 5 100 Coin n/a 50 50

Choose your own settings. See if you can predict the results before running the simulation.