# Histogram

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.

.$h\left(f\right)\left(y\right)$ 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

* [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]

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### Look at other dictionaries:

• histogram — 1891, from HISTO (Cf. histo ) + GRAM (Cf. gram) …   Etymology dictionary

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• histogram — [his′tə gram΄] n. [ HISTO(RY) + GRAM] Statistics a bar graph in which the area of each bar is proportional to the frequency or relative frequency represented …   English World dictionary

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• histogram — A table or bar chart displaying a probability distribution. All of the probabilities in the histogram total to 100 percent. The frequency of the data for each interval is represented by the height of the bar. The technique can be used to combine… …   Financial and business terms

• histogram — /his teuh gram /, n. Statistics. a graph of a frequency distribution in which rectangles with bases on the horizontal axis are given widths equal to the class intervals and heights equal to the corresponding frequencies. [1890 95; HISTO + GRAM1]… …   Universalium

• histogram — UK [ˈhɪstəɡræm] / US [ˈhɪstəˌɡræm] noun [countable] Word forms histogram : singular histogram plural histograms maths a type of bar chart that shows a numerical value on each axis …   English dictionary

• histogram — 1. noun A graphical display of numerical data in the form of upright bars, with the area of each bar representing frequency. 2. verb To represent (data) as a histogram …   Wiktionary

• histogram — s ( met, histogram, best. pl. men) typ av diagram …   Clue 9 Svensk Ordbok

• histogram — histograma statusas T sritis biomedicinos mokslai apibrėžtis ↑Kintamojo reikšmių, grupuotų intervalais, skirstymo grafiškas vaizdavimas stulpeline diagrama. Stulpelio plotis yra proporcingas kintamojo reikšmių intervalui, o aukštis – šių reikšmių …   Lithuanian dictionary (lietuvių žodynas)