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A histogram is a visual representation of the distribution of quantitative data. To construct a histogram, the first step is to "bin" (or "bucket") the range of values— divide the entire range of values into a series of intervals—and then count how many values fall into each interval.
Considerations of the shape of a distribution arise in statistical data analysis, where simple quantitative descriptive statistics and plotting techniques such as histograms can lead on to the selection of a particular family of distributions for modelling purposes. The normal distribution, often called the "bell curve" Exponential distribution
Sturges's rule [1] is a method to choose the number of bins for a histogram.Given observations, Sturges's rule suggests using ^ = + bins in the histogram. This rule is widely employed in data analysis software including Python [2] and R, where it is the default bin selection method.
In the absolutely continuous case, probabilities are described by a probability density function, and the probability distribution is by definition the integral of the probability density function. [7] [4] [8] The normal distribution is a commonly encountered absolutely continuous probability distribution.
Statistical inference is the process of using data analysis to deduce properties of an underlying probability distribution. [29] Inferential statistical analysis infers properties of a population, for example by testing hypotheses and deriving estimates. It is assumed that the observed data set is sampled from a larger population.
Like the statistical mean and median, the mode is a way of expressing, in a (usually) single number, important information about a random variable or a population. The numerical value of the mode is the same as that of the mean and median in a normal distribution , and it may be very different in highly skewed distributions .
where is the standard deviation of the normal distribution and is estimated from the data. With this value of bin width Scott demonstrates that [5] / showing how quickly the histogram approximation approaches the true distribution as the number of samples increases.
Histogram equalization will work the best when applied to images with much higher color depth than palette size, like continuous data or 16-bit gray-scale images. There are two ways to think about and implement histogram equalization, either as image change or as palette change.