Posts Tagged ‘parts’
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 Identify Fractals
Description
A detailed tutorial on fractals. Step by step tutorial including several examples and a helpful visual example of fractals for reference.
Overview
A fractal is a geometric shape that can easily be split into parts. Each part is really just a small version of the whole. Fractals are often very rough or fractured looking shapes, which is how they got their name. The common features of a fractal is that it has a fine structure at small scales, it is an irregular shape, it is self-similar, and it has a recursive definition as well as a simple one. One of the most famous and well-known fractals is the Mandelbrot set.
Tags: fine, fractal, fractured, Geometry, irregular, Mandelbrot, parts, resursive, rough, scale, self, self-similar, shape, similar, simple, small, structure, version
Posted in Geometry | No Comments »
Tuesday, November 10th, 2009
The Numerator and Denominator of a Fraction
Description
A detailed tutorial on the numerator and denominator of a fraction. Step by step tutorial including several examples of numerators and denominators for reference.
Overview
Fractions are well known in the world of mathematics. But when first starting out, you may ask yourself why the fraction appears like it does – split into two parts. You will see a fraction either written horizontal or vertical. In a horizontal fraction, the numerator is the number to the left, and the denominator is the number to the right. In the more common and proper vertical fraction, the numerator is on the top and the denominator is on the bottom. This works when there are whole equations in either the numerator and denominator as well, not just for simpler numbers. The numerator and the denominator should never be split, but algebra tricks can sometimes help to simplify them.
Tags: algebra, arithmetic, bar, denominator, equations, fraction, horizontal, number, numerator, parts, simplify, split, tricks, two, vertical
Posted in Arithmetic | No Comments »
Friday, October 30th, 2009
Overview of Summation by Parts
Description
A detailed tutorial on summation by parts. Step by step tutorial including several examples of summation by parts for reference.
Overview
Summation by parts transforms the summation of products of sequences into other summations. Often it will simplify the computation of certain sums. Summation by parts is also referred to as Abel’s lemma or Abel’s transformation. Summation by parts is similar to integration by parts, only by using summation instead of integration. In mathematical notation, summation by parts can be written as: ![\sum_{k=m}^n f_k(g_{k+1}-g_k) = \left[f_{n+1}g_{n+1} - f_m g_m\right] - \sum_{k=m}^n g_{k+1}(f_{k+1}- f_k)](http://s.wordpress.com/latex.php?latex=%5Csum_%7Bk%3Dm%7D%5En%20f_k%28g_%7Bk%2B1%7D-g_k%29%20%3D%20%5Cleft%5Bf_%7Bn%2B1%7Dg_%7Bn%2B1%7D%20-%20f_m%20g_m%5Cright%5D%20-%20%5Csum_%7Bk%3Dm%7D%5En%20g_%7Bk%2B1%7D%28f_%7Bk%2B1%7D-%20f_k%29&bg=ffffff&fg=000000&s=0 "\sum_{k=m}^n f_k(g_{k+1}-g_k) = \left[f_{n+1}g_{n+1} - f_m g_m\right] - \sum_{k=m}^n g_{k+1}(f_{k+1}- f_k)")
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Tags: Abel, algebra, computation, integration, lemma, mathematical, parts, product, sequence, sum, summation, transformation
Posted in Algebra | No Comments »
