Description
A detailed tutorial on direct variation. Step by step tutorial including several examples of direct variation and what direct variation is for reference.
Overview
Direct variation states that given two variables x and y, y is directly proportional to x if there is a non-zero constant k such that y = k * x. The variable k is referred to as the proportionality constant or the constant of proportionality.
Description
A detailed tutorial on combined variation. Step by step tutorial including several examples of combined variation and what combined variation is for reference.
Overview
Combined variation refers to using both direct variation and inverse variation at the same time. Combined variation can be expressed as y = (k * x) / (z^2). Typically when both direct and inverse variation are being used, the same variable will variate directly at one point and inversely at another.
Description
A detailed tutorial on joint variation. Step by step tutorial including several examples of joint variation and what joint variation is for reference.
Overview
Joint variation is the same as direct variation, only it is occuring for more than one variable, while direct variation only deals with one variable. Because of the similarities, joint variation is performed in the same way as direct variation, although for two variables and not one. Joint variation can be expressed as d = r * t.
Description
A detailed tutorial on how to make tree diagrams. Step by step tutorial including several examples of how to make tree diagrams for reference.
Overview
A tree diagram is a specific type of diagram that is often used to organize items and possibilities. It has a unique network topology. It can be seen as a type of network diagram, which can in turn be seen as a cluster diagram. Tree diagrams are very useful when trying to figure out probabilities and statistics.
Description
A detailed tutorial on the solving of Averages in Statistics. Step by step tutorial including several examples of how to solve Averages in Statistics for reference.
Overview
The average (also know as mean), is obtained by dividing the sum of observed values by the number of observations, n. Although data points fall above, below, or on the mean, it can be considered a good estimate for predicting subsequent data points.
Description
A detailed tutorial on the Law of Large Numbers. Step by step tutorial including several examples of the Law of Large Numbers for reference.
Overview
The Law of Large Numbers, or the LLN, is a theorem in probability and statistics that refers to how long the mean of the possible choices for a random variable will remain the same. It is called the “stability” of the mean. Rolling a die is the best example of the Law of Large Numbers; although the numbers on the die are not large, no matter what the outcome is the mean is always the same. Anything with a set amount of possibilities like that, such as flipping a coin, would have the same result with the stability of the mean.
Description
A detailed tutorial on the solving of Expected Value. Step by step tutorial including several examples of how to solve Expected Value for reference.
Overview
The expected value of a variable is the integral of the variable with respect to its probability measure. It amounts to either the probability-weighted sum or the probability-weighted integral of all possible values of the variable, depending on whether you are using it for discrete random variables or continuous random variables. The expected value does not exist for all variables, but it is always the limit of a sample mean, or average, of the possible solutions for the variable.
Description
A detailed tutorial on the solving of combinations. Step by step tutorial including several examples of how to solve combinations for reference.
Overview
Combinations are often used with permutations. A combination is actually just the written representation of the permutation – with the permutation, you figure out how many different combinations there are, but with combinations you actually write down what those combinations are, not just how many there is. Many people prefer permutations because permutations are a lot less work. However, combinations do come up frequently, most notably in logic courses like discrete math.
Description
A detailed tutorial on the solving of permutations. Step by step tutorial including several examples of how to solve permutations for reference.
Overview
A permutation is an ordered sequence of elements, also known as a set. Basically, a permutation is when you have a set amount of possibilities to be one thing (typically a variable), and then you have one less than that number of possibilities for your next variable, etc. Often you can use this to figure out exactly how many possible combinations in a set there are. Permutations are used very often in math, all done slightly different depending on the branch of mathematics, but it is first introduced in precalculus.
