Probability is straightforward: you have the bear. Measure the foot size, the leg length, and you can deduce the footprints.
A Brief Introduction to Probability & Statistics
Bubbles weighs lbs and has 3-foot legs, and will make tracks like this. After 10 flips, here are the possible outcomes. Statistics is harder. We measure the footprints and have to guess what animal it could be. A bear? A human? If we get 6 heads and 4 tails, what're the chances of a fair coin?
Get the tracks. Each piece of data is a point in "connect the dots".
The more data, the clearer the shape 1 spot in connect-the-dots isn't helpful. One data point makes it hard to find a trend. Measure the basic characteristics. Every footprint has a depth, width, and height.
Every data set has a mean , median, standard deviation, and so on. These universal, generic descriptions give a rough narrowing: "The footprint is 6 inches wide: a small bear, or a large man?
Probability and statistics - Wikipedia
Find the species. There are dozens of possible animals probability distributions to consider. We narrow it down with prior knowledge of the system. In the woods? Think horses, not zebras. Consider a binomial distribution. Look up the specific animal. Once we have the distribution "bears" , we look up our generic measurements in a table.
The lookup table is generated from the probability distribution, i. Make additional predictions. Once we know the animal, we can predict future behavior and other traits "According to our calculations, Mr. Bubbles will poop in the woods. The conditions under which data are collected are important in drawing conclusions from the data; in critically reviewing uses of statistics in public media and other reports, it is important to consider the study design, how the data were gathered, and the analyses employed as well as the data summaries and the conclusions drawn.
Random processes can be described mathematically by using a probability model: a list or description of the possible outcomes the sample space , each of which is assigned a probability. In situations such as flipping a coin, rolling a number cube, or drawing a card, it might be reasonable to assume various outcomes are equally likely. In a probability model, sample points represent outcomes and combine to make up events; probabilities of events can be computed by applying the Addition and Multiplication Rules. Interpreting these probabilities relies on an understanding of independence and conditional probability, which can be approached through the analysis of two-way tables.
Technology plays an important role in statistics and probability by making it possible to generate plots, regression functions, and correlation coefficients, and to simulate many possible outcomes in a short amount of time. Functions may be used to describe data; if the data suggest a linear relationship, the relationship can be modeled with a regression line, and its strength and direction can be expressed through a correlation coefficient.
Connections to Functions and Modeling Functions may be used to describe data; if the data suggest a linear relationship, the relationship can be modeled with a regression line, and its strength and direction can be expressed through a correlation coefficient. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics.
Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning.