Posts Tagged ‘set’
Friday, November 13th, 2009
How to Find the Interquartile Range
Description
A detailed tutorial on how to find the interquartile range. Step by step tutorial including several examples of the interquartile range for reference.
Overview
The interquartile range is the range of the data between the lower or first quartile and the upper or third quartile. The interquartile range is not the whole data set – it is actually only half of the data set, although not a common half – the first and last quarter of the data is not included in the interquartile range. To find the interquartile range, all you must do is find all the quartiles, and then find the different between the upper quartile and lower quartile.
Tags: data, First, half, interquartile, lower, median, quarter, quartile, range, second, set, statistics, third, upper
Posted in Statistics | No Comments »
Friday, November 13th, 2009
Definition of a Quartile
Description
A detailed tutorial on the definition of a quartile. Step by step tutorial including several examples of the definition of a quartile for reference.
Overview
A quartile is a value that separates out statistical data. There are three quartiles, and they work together to separate data out into four different parts. The first quartile, called Q1, is the lower quartile. It is the 25th percentile of data – that is, the median of the median of the total amount of data, and the lowest count in a data set. The second quartile, called Q2, is the median of the entire data set. It is sometimes referred to as the middle value. The third quartile, called Q3, is the upper quartile. It is the 75th percentile of data – that is, the median of the median of the total amount of data, and the highest count in a data set.
Tags: 25, 50, 75, data, First, lower, median, middle, parts, percentile, Q1, Q2, Q3, quartile, second, separate, set, statistical, statistics, third, upper
Posted in Statistics | No Comments »
Thursday, November 12th, 2009
How to Make a Histogram
Description
A detailed tutorial on how to make a histogram. Step by step tutorial including several examples on how to make a histogram for reference.
Overview
A histogram is similar to a bar chart or bar graph, only it cannot go in either direction – histograms can only have vertical bars. The main difference between them is that bar charts and bar graphs can be used to show the number of items in a category. Histograms are used between two sets of numbers, to show which numbers relate to each other. The numbers themselves each fall under their own category. This is a very common chart to see in the later levels of math, especially statistics, as they reflect statistical data.
Tags: algebra, bar, category, chart, data, difference, graph, histogram, horizontal, number, relationship, set, statistics, vertical
Posted in Algebra | No Comments »
Tuesday, November 10th, 2009
How to Make a Circle Graph
Description
A detailed tutorial on how to make circle graphs. Step by step tutorial including several examples of how to make circle graphs for reference.
Overview
Circle graphs, also referred to as pi charts to avoid confusing them with graphs on the coordinate plane, are graphs in the shape of a circle that deal with a specific set of data. Circle graphs deal with percentages of a whole. The title of the circle graph is your whole, and the circle represents the whole. Then the circle is cut off into different percentages, and each is labelled with the proper category and exactly what percent it is meant to represent. Very often each section of the circle will be a different color to avoid confusion.
Tags: algebra, categories, category, chart, circle, color, data, different, graph, label, percent, percentage. title, pi, represent, section, set
Posted in Algebra | No Comments »
Tuesday, November 10th, 2009
How to Make a Bar Graph
Description
A detailed tutorial on how to make bar graphs. Step by step tutorial including several examples on how to make a bar graph for reference.
Overview
A bar graph, also referred to as a bar chart as to not be confused with graphs on the coordinate plane, is a visual expression of a set of data. Bar graphs deal with the real numbers in specific data sets. Typically they are split up into more than one category. A bar is drawn on each category extending to the number associated with that category. Traditionally, bar graphs need to have a title, an assigned label to each axis, and a certain pattern to continue writing numbers in.
Tags: algebra, axis, bar, categories, category, chart, graph, label, number, pattern, set, title, visual
Posted in Algebra | No Comments »
Friday, November 6th, 2009
Overview of Orthogonal Complements
Description
A detailed tutorial on orthogonal complements. Step by step tutorial including several examples of orthogonal complements for reference.
Overview
The orthogonal complement of a subspace of an inner product space is the set of all vectors in the inner product space that are orthogonal to every vector in the subspace. This can be expressed mathematically in the formula 
, where W is the subspace and V is the inner product space. The orthogonal complement is sometimes also called the perpendicular complement, shortened to the informal form perp.
Tags: algebra, complement, formula, inner, orthogonal, perp, perpendicular, product, set, space, subspace, v, vector, W
Posted in Algebra | No Comments »
Thursday, November 5th, 2009
How to Use Parametrization
Description
A detailed tutorial on how to use parametrization. Step by step tutorial including several examples of how to use parametrization for reference.
Overview
Parametrization can be used in many different branches of math, including algebra and calculus. Parametrization involves setting up parameters necessary for the complete or relevent specification of a geometric object. This means it is only used when calculating a shape or part of a shape, because that is what a geometric object is. Sometimes, this is nothing more than identifying the parameters. Other times it becomes an involved mathematical process that is used to find out what the parameters are.
Tags: Calculus, complete, decide, deciding, define, defining, differential equations, geometric, identify, identifying, parameter, parametrization, relevent, set, setting, shape, specification, vector
Posted in Differential Equations | No Comments »
Thursday, November 5th, 2009
Introduction to Nested Intervals
Description
A detailed tutorial on nested intervals and the nested interval theorem. Step by step tutorial including several examples of nested intervals for reference.
Overview
Nested intervals means to have one interval (or multiple intervals) inside of another interval. The intervals will get smaller and smaller the more you add, until they will finally dimish entirely. There is a theorem for nested intervals, called the nested interval theorem. It states that if A_n = [a_n, b_n] is a sequence of closed intervals such that A_n+1 is a subset of A_n for all n belonging to the set of natural numbers, then the union over A_n is not an empty set.
Tags: algebra, closed, empty, interval, natural, nested, number, open, sequence, set, subset, theorem
Posted in Algebra | No Comments »
Thursday, November 5th, 2009
Linear Subspaces Explained
Description
A detailed tutorial on linear subspaces and how to identify linear subspaces. Step by step tutorial including several examples of linear subspaces for reference.
Overview
A linear subspace is usually referred to as simply a subspace, when it needs to be distinguished from other types of subspaces. Linear subspaces are also sometimes referred to as vector subspaces. In mathematical terms, to identify a linear subspace, we say that K is a field (or a set, like of real numbers), and V is a vector space over K. Elements of V are vectors and elements of K are scalars. W is said to be a subset of V. If W is a vector space itself, with the same vector space operations as V, then it has a subspace of V.
Tags: algebra, element, field, k, linear, number, operations, real, scalar, set, space, subset, subspace, v, vector, W
Posted in Algebra | No Comments »
Tuesday, November 3rd, 2009
Well-Ordering Principle Explained
Description
A detailed tutorial on the well-ordering principle. Step by step tutorial including several examples of the well-ordering principle for reference.
Overview
The well-ordering principle states that every nonempty subset of the set of all natural numbers has a smallest element. This is possible because the number zero is not included in the set of natural numbers, and therefore cannot appear in a subset of all natural numbers. The well-ordering principle is equivalant to the Principle of Mathematical Induction, but they are proved in different ways and have different sets. Sometimes it is a better idea to use the Well-Ordering Principle, and other times it is a better idea to use the Principle of Mathematical Induction.
Tags: discrete math, element, induction, mathematical, n!, natural, nonempty, number, ordering, PMI, principle, set, smallest, subset, well, well-ordering, WOP
Posted in Discrete Math | No Comments »
