Equal Intervals
Equal intervals is a method used for classifying numeric data, particularly within the fields of geographic information technology and geographic information systems. This approach organizes data into distinct classes that are visually represented on classified maps, which utilize color coding or variations in shade and brightness to improve the clarity of the information being presented. The main advantage of equal intervals is that it simplifies the visualization of data by ensuring each class represents an equal range of values.
To create these classes, the overall data range (the difference between the highest and lowest values) is divided by the desired number of classes. For example, if analyzing distances students live from a school, the data could be segmented into equal intervals, allowing for clear distinctions among groups based on distance. While equal intervals is commonly employed in geographic data analysis, it can be applied to any numeric dataset. Alternative classification methods include mean-standard deviation, quantiles, maximum breaks, and natural breaks, each with its own approach to data segmentation.
On this Page
Subject Terms
Equal Intervals
An interval is the set of real numbers between and including two given numbers. The real numbers, as a set, are themselves an interval, as is the empty set, or the set of all negative real numbers. Another interval set would be the numbers between (and including) 2 and 3. Intervals are usually written [a, b], for a set consisting of greater than or equal to a and less than or equal to b. The interval's endpoints are a and b.
In some mathematics publications, a semicolon is used instead of a comma to separate the endpoints, because some countries write numbers with a decimal comma. A reversed bracket can be used to indicate that an endpoint is excluded from the interval: ]a, b] is the interval consisting of the set of numbers greater than a and less than or equal to b. Sometimes parentheses are used to indicate this instead, especially for intervals that exclude both endpoints. In programming contexts in particular, an interval may sometimes be declared to consist only of the integers in a set, which is declared with the notation [a .. b] or sometimes just a .. b.
Overview
Equal intervals is a method of classifying data in geographic information technology and geographic information systems. To properly analyze numeric geographical data, this data is often classified first by one of various methods to create a classified map. A classified map is one that represents geographic data sorted into classes distinguishable by color coding (or shade, brightness, and saturation). Classification helps to limit the number of data classes to a level clearly distinguished by the human eye, so that large distinctions are not missed amid a muddle of smaller distinctions.
While common in analyzing geographical data, this method of classification can be used for any kind of numeric data. Equal intervals is a major method of classifying data for such purposes. Each class in this method consists of an equal data interval along a dispersion graph, according to the number of classes the preparer has decided to generate. The interval of each class consists of the data range (the highest value minus the lowest value) divided by the number of classes. For instance, if sorting students into groups according to how far away from school they live, the shortest distance of 0.1 miles is subtracted from the greatest distance of 15.3 miles, resulting in a range of 15.2 miles. If the preparer wants to sort students into five groups, each group would consist of an equal interval of 3.04 miles: Where x = the distance a student lives from school, Class A is [0.1, 3.14], Class B is [3.14, 6.18], Class C is [6.18, 9.22], Class D is [9.22, 12.26], and Class E is [12.26, 15.3].
Other methods of classifying such data are the mean-standard deviation classification, quantiles, maximum breaks, and natural breaks.
Bibliography
Aigner, Martin, and Gunter M. Ziegler. Proofs from the Book. New York: Springer, 2014.
Grunbaum, Branko, and G. C. Shephard. Tilings and Patterns. New York: Dover, 2015.
Hanna, Gila. Explanation and Proof in Mathematics. New York: Springer, 2014.
Kahn, David. Attacking Trigonometry Problems. New York: Dover, 2015.
Larson, Ron. Algebra and Trigonometry. Boston: Cengage, 2015.
Millman, Richard, Peter Shiue, and Eric Brendan Kahn. Problems and Proofs in Numbers and Algebra. New York: Springer, 2015.