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The data used to construct a histogram are generated via a function m i that counts the number of observations that fall into each of the disjoint categories (known as bins). Thus, if we let n be the total number of observations and k be the total number of bins, the histogram data m i meet the following conditions:
where is the interquartile range of the data and is the number of observations in the sample . In fact if the normal density is used the factor 2 in front comes out to be ∼ 2.59 {\displaystyle \sim 2.59} , [ 4 ] but 2 is the factor recommended by Freedman and Diaconis.
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In addition, the choice of appropriate statistical graphics can provide a convincing means of communicating the underlying message that is present in the data to others. [1] Graphical statistical methods have four objectives: [2] The exploration of the content of a data set; The use to find structure in data; Checking assumptions in statistical ...
The left histogram appears to indicate that the upper half has a higher density than the lower half, whereas the reverse is the case for the right-hand histogram, confirming that histograms are highly sensitive to the placement of the anchor point. [6] Comparison of 2D histograms. Left. Histogram with anchor point at (−1.5, -1.5). Right.
In image processing, histogram matching or histogram specification is the transformation of an image so that its histogram matches a specified histogram. [1] The well-known histogram equalization method is a special case in which the specified histogram is uniformly distributed .
In more general fields of data processing, such as digital signal processing, it is referred to as dynamic range expansion. [ 1 ] The purpose of dynamic range expansion in the various applications is usually to bring the image, or other type of signal, into a range that is more familiar or normal to the senses, hence the term normalization.