# Using Polypad: Probability and Data

## Introduction

This tutorial provides an overview of the Probability Tiles. Below are the topics covered.

• Coins, Dice, Spinners, and Random Numbers
• Sound Effects
• Charts and Statistics
• Playing Cards
• Probability Tiles on the Balance Scale

## Coins, Dice and Spinner

Copy tiles to easily create multiple coins and dice. Move the black circle on the uniform spinner to change the number of regions. Move the black circles on the custom spinner to change the size of the regions. Click on the black circle to add a region and click on a black circle to remove a region.

## Custom Spinners

Add labels to spinners to create custom spinners.

## Random Numbers

There are 9 different distributions for the Random Number tile. For some of the more advanced distributions, only a brief overview is provided below. Further study and exploration may be needed for a thorough understanding of specific distribution.

• Discrete Uniform: Enter in a minimum and maximum number. Entries can range from -100 quadrillion to 100 quadrillion. Clicking Randomize will return an integer within the selected range.
• Bernoulli: Enter a value for p to define the probability that a “1” will appear. Clicking Randomize will return a “1” with probability p and a “0” with probability 1-p. Click here to read more.
• Binomial: Enter a value for p to define the probability that an event will result in a favorable outcome. Enter a value for n to define the number of trials of an event to perform. Clicking Randomize will return the number of favorable outcomes out of the total trials performed. For example, say p = 0.50, n = 100 and clicking Randomize returns “55” on the tile. That means that of the 100 trials, each with a 0.50 chance of coming up favorable, 55 out of the 100 resulted in a favorable outcome. Click here to read more.
• Poisson: Enter a value for λ to define the expected number of occurrences of an event. Clicking Randomize will return a number of occurrences according to the Poisson distribution model. Click here to read more.
• Geometric: Enter a value for p to define the probability that an event will result in a favorable outcome. Clicking Randomize will return the total number of times the event was needed to be performed until a favorable result appeared. For example, a 0 appearing upon clicking Randomize means the event returned a favorable outcome on the first trial of the event. A 1 appearing upon clicking Randomize means the event returned a favorable outcome on the second trial of the event, a 2 appearing upon clicking Randomize means the event returned a favorable outcome on the third trial of the event, and so on. Click here to read more.
• Continuous Uniform: Enter in a minimum and maximum number. Entries can range from -100 quadrillion to 100 quadrillion. Clicking Randomize will return a rational number within the selected range. Polypad will round the number as needed in order to fit the digits in the tile.
• Normal: Enter μ to define the mean or expected value and enter $σ^2$ to define the variance of the distribution with a standard deviation of $σ$. Clicking randomize will return a value according the normal distribution model. Click here to read more.
• Exponential: Enter a value for λ to set a mean or expected value of $1/λ$ and a variance of $1/λ^2$. Clicking Randomize will return a value according to this mean and variance. Click here to read more.
• Cauchy: There are not any parameters to change in this distribution. Click here to read more.

## Sound Effects

Sound effects are available for most probability tools as well as merging Number Cards. Sound effects can be turned on and off in the Customize UI settings menu.

## Charts and Statistics

After creating a data table, place a chart type on the canvas and use the blue triangular handle to link the data table to a chart type.

### Column and Row Charts

Column and Row charts can be displayed in grouped, stacked, or percentage mode. Double click on one of the bars to change the color for all bars of that series.

### Line Charts

Double click on a line to change the color. Line charts can also be displayed as area charts. Hide a row or column in the table to hide that data from the chart. Add data to the table to display new data in the chart.

### Pie and Donut Charts

Double click on a region of the chart to change the color. Display the data as a pie chart or donut chart. Change the data in the table to change the chart. Add or remove data from the table to add or remove it from the chart.

### Box and Whisker Plots

Double click on a chart to change the color. Use the "Toggle Outliers" button to switch between displaying outliers as either part of the plot or as a separate point. An outlier is any data point which is more than 1.5 times the interquartile range above the third quartile or below the first quartile. Add or remove data from the table to add or remove it from the chart. If no outliers exist, the "Toggle Outliers" button will not show any changes.

### Multiple Charts from One Data Table

Create multiple charts from the same data table:

## Playing Cards

• Drag cards on top of each other to create a stack of cards. Selecting the stack reveals the number of cards in the stack.
• Select the Deck of 52 from the tile menu to place a full deck on the canvas.
• Select multiple cards and click Stack to place them in one pile.
• With a single card selected, click Turn Over to flip that card.
• With a stack of cards selected, click Turn Over to flip over the entire stack. If the stack is face-up, clicking Turn Over will result in the face-up card being on the bottom of the face-down stack. Clicking Turn Over flips the entire stack.
• Click Draw to remove the top card from a stack. Double-clicking on a stack also draws the top card.
• Clicking Shuffle only shuffles cards in a stack.

## Rolling, Spinning, and Flipping

Double-click dice, coins and spinners to randomize. Double-click playing cards to draw a card.

## Probability Tiles on the Balance Scale

The Dice and Playing Cards can be used on the Balance Scale