Posts Tagged ‘average’
Thursday, October 1st, 2009
Definition of a Cissoid
Description
A detailed tutorial of the definition of a cissoid. Step by step tutorial including a visual example of the definition of a cissoid for reference.
Overview
A cissoid is a curve that is found from two curves and a point. The point is known as “the pole”. Each definition of a cissoid and instructions on how to find the cissoid are a little different, depending on your source. However, the basic definition of a cissoid is that it is an average point that is relative to the pole and found between the two given curves. Keep in mind that the cissoid is a curve, not a point, but the curve is to be drawn from the point that is found.
Tags: average, cissoid, curve, Geometry, line, locus, Math, point, polar coordinates, pole, relative
Posted in Geometry | No Comments »
Friday, September 18th, 2009
How to calculate the Average of a set of numbers?
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.
Tags: arithmetic mean, average, Math, statistics
Posted in Statistics | No Comments »
Thursday, September 17th, 2009
Law of Large Numbers Explained
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.
Tags: average, expected, expected value, law of large numbers, Math, mean, possibilities, probability, random, statistics, value, variable
Posted in Statistics | No Comments »
Thursday, September 17th, 2009
Definition of Expected Value
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.
Tags: average, continuous, discrete math, expected, expected value, limit, Math, mean, probability, random, sample, solutions, statistics, value, variable
Posted in Statistics | No Comments »
Thursday, September 17th, 2009
Definition of the Mean Value Theorem
Description
A detailed tutorial on the solving of the Mean Value Theorem. Step by step tutorial including several examples of how to solve the Mean Value Theorem for reference.
Overview
You can easily figure out what the Mean Value Theorem is by looking at the word mean – a mean is an average. The Mean Value Theorem states that there is at least one point on the graph of a function where the derivative is equal to the average slope of the entire section of the graph you are looking at. The requirements are that the graph is both continuous and differentiable on the interval [a, b], where a < b. Then there exists some c in (a, b) such that:
f ‘(c) = [f(b) - f(a)] / [b - a]
The Mean Value Theorem is very similar to Rolle’s Theorem, which is a more specific theorem stating the same thing.
Tags: a, average, b, c, Calculus, continuous, derivative, differentiable, interval, Math, mean, mean value theorem, rolle's theorem, slope, theorem, value
Posted in Calculus | No Comments »
