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Whereas statistics and data analysis procedures generally yield their output in numeric or tabular form, graphical techniques allow such results to be displayed in some sort of pictorial form. They include plots such as scatter plots , histograms , probability plots , spaghetti plots , residual plots, box plots , block plots and biplots .
A scatter plot, also called a scatterplot, scatter graph, scatter chart, scattergram, or scatter diagram, [2] is a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data. If the points are coded (color/shape/size), one additional variable can be displayed.
If a chart plots 10 colors or fewer, then by default it uses every other one: The colors can be manually set in a graph by adding them to the 'colors' parameter. For example, for two pie charts, the first of which is default and the second of which omits some colors in the first, you would manually enter your selections from the default 20:
cluster heat map: where magnitudes are laid out into a matrix of fixed cell size whose rows and columns are categorical data. For example, the graph to the right. spatial heat map: where no matrix of fixed cell size for example a heat-map. For example, a heat map showing population densities displayed on a geographical map; Stripe graphic ...
The graphs can be used together to determine the economic equilibrium (essentially, to solve an equation). Simple graph used for reading values: the bell-shaped normal or Gaussian probability distribution, from which, for example, the probability of a man's height being in a specified range can be derived, given data for the adult male population.
A probability-based survey sample is created by constructing a list of the target population, called the sampling frame, a randomized process for selecting units from the sample frame, called a selection procedure, and a method of contacting selected units to enable them to complete the survey, called a data collection method or mode. [10]
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As Murty's survey paper [1] notes, Ramanujan graphs "fuse diverse branches of pure mathematics, namely, number theory, representation theory, and algebraic geometry". These graphs are indirectly named after Srinivasa Ramanujan; their name comes from the Ramanujan–Petersson conjecture, which was used in a construction of some of these graphs.