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# What is a histogram useful for?

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Histograms are useful in pictorial representations of data distributions. The histogram is a type of bar graph, where bar height or length represents the frequency of occurrence of a continuous distribution of data classes.

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Histograms show basic information about the data set, such as the median data value, the width of spread and the overall distribution of the quality being displayed. Histograms can be used to assess the current state of a system, compare this state with historical data and make inferences about how the system is likely to evolve.

Histograms can be created directly from discrete data or from continuous data by first sorting this data into bins. Bins are regular intervals representing different ranges for the class of data being plotted. Dividing ages between 30 and 50 into sequential intervals of five years is an example of bins.

The individual values that satisfy the criteria of the bin are called scores. The scores of values for each bin are tallied. Values that fall right at the edge between two bins are consistently rounded up or down. Plotting bin values against the frequency of their occurrence in the form of bars gives the histogram. The bars of a histogram represent continuous data, so there should be no gaps between them.

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## Related Questions

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Vectors can be added graphically by beginning the points of the vectors in a direction that is similar to walking and allowing the points between the vectors to be the distance between them. In order for vectors to be added graphically, they must first be added mathematically to ensure that they are in the right coordinates.

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The purpose of a frequency polygon is to communicate the shape of distributions. The purpose is similar to that of a histogram but is preferable when it comes to providing data comparisons. Those needing to display cumulative frequency distributions also find frequency polygrams to be more helpful.

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A covariance matrix is a P*P matrix with elements from a vector of random variables. The element in the position i, j is the given covariance between the ith and jth elements. The covariance matrix can also be referred to as the variance-covariance matrix or the dispersion matrix. The concept of covariance matrix enhances the general idea of variance in multiple dimensions.