Histogram

In statistics, a histogram is a graphical display of tabulated frequencies, shown as bars. It shows what proportion of cases fall into each of several categories. A histogram differs from a bar chart in that it is the "area" of the bar that denotes the value, not the height, a crucial distinction when the categories are not of uniform width (Lancaster, 1974). The categories are usually specified as non-overlapping intervals of some variable. The categories (bars) must be adjacent.

The word "histogram" is derived from Greek: "histos" 'anything set upright' (as the masts of a ship, the bar of a loom, or the vertical bars of a histogram); "gramma" 'drawing, record, writing'. The histogram is one of the seven basic tools of quality control, which also include the Pareto chart, check sheet, control chart, cause-and-effect diagram, flowchart, and scatter diagram. A generalization of the histogram is kernel smoothing techniques. This will construct a very smooth probability density function from the supplied data.

Examples

As an example we consider data collected by the U.S. Census Bureau on time to travel to work (2000 census, [http://www.census.gov/prod/2004pubs/c2kbr-33.pdf] , Table 5). The census found that there were 124 million people who work outside of their homes. This rounding is a common phenomenon when collecting data from people.

.$h(f)(y)$ is undefined if $y$ is the value of a stationary point.

ee also

* Density estimation
* Freedman-Diaconis rule
* Image histogram
* Kernel density estimation , another method of visualizing probability density functions that can be preferred to histograms.

Notes

References

*Webster's Third New International Dictionary, "Merriam-Webster; Ind Una edition (June 2002)".
* Lancaster, H.O. "An Introduction to Medical Statistics." John Wiley and Sons. 1974. ISBN 0 471 51250-8

External links

* [http://www.census.gov/population/www/socdemo/journey.html Journey To Work and Place Of Work] "(location of census document cited in example)"
* [http://www.luminous-landscape.com/tutorials/understanding-series/understanding-histograms.shtml Understanding histograms in digital photography]
* [http://quarknet.fnal.gov/toolkits/ati/histograms.html Histograms: Construction, Analysis and Understanding with external links and an application to particle Physics.]
* [http://www.ton.scphys.kyoto-u.ac.jp/~hideaki/res/histogram.html A Method for Selecting the Bin Size of a Histogram]
* [http://www.shodor.org/interactivate/activities/histogram/ Interactive histogram generator]