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Histogram
Histogram of arrivals per minute.svg
One of the Seven Basic Tools of Quality
First described by Karl Pearson
Purpose To roughly assess the probability distribution of a given variable by depicting the frequencies of observations occurring in certain ranges of values
.In statistics, a histogram is a graphical display of tabular frequencies, shown as adjacent rectangles.^ The following histogram displays the number of books on the x-axis and the frequency on the y-axis.
  • Descriptive Statistics: Histogram 23 January 2010 4:55 UTC cnx.org [Source type: General]

^ The following histogram displays the heights on the x-axis and relative frequency on the y-axis.
  • Descriptive Statistics: Histogram 23 January 2010 4:55 UTC cnx.org [Source type: General]

^ Purpose Of A Histogram A histogram is used to graphically summarize and display the distribution of a process data set.

Each rectangle is erected over an interval, with an area equal to the frequency of the interval. The height of a rectangle is also equal to the frequency density of the interval, i.e. the frequency divided by the width of the interval. The total area of the histogram is equal to the number of data. .A histogram may also be based on the relative frequencies instead.^ In this type of bivariate histogram , the frequencies are represented as a series of "spikes" (point symbols with lines descending to the base plane).
  • Statistics Glossary: H 23 January 2010 4:55 UTC www.statsoft.com [Source type: Academic]

^ Shape is Relative You may have heard that a good histogram has a smooth, bell curve shape.

^ The following histogram displays the heights on the x-axis and relative frequency on the y-axis.
  • Descriptive Statistics: Histogram 23 January 2010 4:55 UTC cnx.org [Source type: General]

.It then shows what proportion of cases fall into each of several categories (a form of data binning), and the total area then equals 1. The categories are usually specified as consecutive, non-overlapping intervals of some variable.^ What if no data fall in a given bin?
  • JD Smith's Histogram Tutorial: The Breathless Horror and Disgust 23 January 2010 4:55 UTC www.dfanning.com [Source type: FILTERED WITH BAYES]

^ There is 300 mm available travel.  The software might divide the travel into 30 equal "bins" of 10 mm.  The first bin is 0 to 10, the second is 10 to 20, the third is 20 to 30, etc.  Every data point within the bins "Range" (0-10, 10-20, etc.
  • Welcome To ShockClock - 6.2.3 Travel Histogram 23 January 2010 4:55 UTC new.racetech.com [Source type: Reference]

^ For example, the following code sorts DAT1 values into five equally sized bins in the value range from 0.
  • Chapter 17: Creating bar charts using the Histogram utility 23 January 2010 4:55 UTC ngwww.ucar.edu [Source type: Reference]

The categories (intervals) must be adjacent, and often are chosen to be of the same size,[1] but not necessarily so.
.Histograms are used to plot density of data, and often for density estimation: estimating the probability density function of the underlying variable.^ Can I apply the proposed method of a histogram to estimate a probability (density) distribution?

^ To draw histogram, use the original data.

^ Calculate the cumulative density function of the histogram.
  • Contrast Enhancement through Localized Histogram Equalization 23 January 2010 4:55 UTC www.cromwell-intl.com [Source type: FILTERED WITH BAYES]

.The total area of a histogram used for probability density is always normalized to 1. If the length of the intervals on the x-axis are all 1, then a histogram is identical to a relative frequency plot.^ Compute the total area under the histogram.
  • contrib/gel/vifa: vifa_histogram Class Reference 23 January 2010 4:55 UTC www.lems.brown.edu [Source type: Reference]
  • contrib/gel/vifa: vifa_histogram Class Reference 23 January 2010 4:55 UTC public.kitware.com [Source type: Reference]

^ The following histogram displays the heights on the x-axis and relative frequency on the y-axis.
  • Descriptive Statistics: Histogram 23 January 2010 4:55 UTC cnx.org [Source type: General]

^ Total area under the histogram.
  • contrib/brl/bbas/bsta: bsta_histogram< T > Class Template Reference 23 January 2010 4:55 UTC www.lems.brown.edu [Source type: Reference]

.An alternative to the histogram is kernel density estimation, which uses a kernel to smooth samples.^ Fit nonparametric kernel density estimates .
  • The UNIVARIATE Procedure : HISTOGRAM Statement 23 January 2010 4:55 UTC www.uc.edu [Source type: Reference]

^ Which of the methods, a histogram or kernel, is good for density estimation?

^ A. We generally recommed to use the kernel density estimate.

.This will construct a smooth probability density function, which will in general more accurately reflect the underlying variable.^ It defines a function used by the template program to generate the various function and type names derived from the name of the header record type, i .
  • Pads Manual: Chapter 17  Histogram 23 January 2010 4:55 UTC www.padsproj.org [Source type: FILTERED WITH BAYES]

^ F(t) are the probability density and cumulative distribution functions, respectively.
  • Statistics Glossary: H 23 January 2010 4:55 UTC www.statsoft.com [Source type: Academic]

^ It defines a function used by the template program to generate the various function and type names derived from the name of the record type, i .
  • Pads Manual: Chapter 17  Histogram 23 January 2010 4:55 UTC www.padsproj.org [Source type: FILTERED WITH BAYES]

.The histogram is one of the seven basic tools of quality control.^ Creative Use of Depth of Field Control of depth-of-field is one of the most creative tools photographers have.
  • Learning to Use the Histogram from Nikon 23 January 2010 4:55 UTC www.nikonusa.com [Source type: General]

^ Learning to use the basic exposure modes and the histogram requires just a little of patience and practice, but it gives complete control on the image.
  • Juza Nature Photography 23 January 2010 4:55 UTC www.juzaphoto.com [Source type: FILTERED WITH BAYES]

[2]

Contents

Etymology

An example histogram of the heights of 31 Black Cherry trees.
The word histogram derived from the Greek histos 'anything set upright' (as the masts of a ship, the bar of a loom, or the vertical bars of a histogram); and gramma 'drawing, record, writing'. The term was introduced by Karl Pearson in 1895.[3]

Examples

.As an example we consider data collected by the U.S. Census Bureau on time to travel to work (2000 census, [1], Table 2).^ The data is an example from Neuroscience: a timing of neuronal firing (spikes) obtained by repeating trials.

^ Most people are accustomed to seeing Travel data displayed with respect to Time.  A histogram displays data with respect to number of occurrences instead of Time.
  • Welcome To ShockClock - 6.2.3 Travel Histogram 23 January 2010 4:55 UTC new.racetech.com [Source type: Reference]

.The census found that there were 124 million people who work outside of their homes.^ If you fall into the class of people who believe that the more information you have to work with, the better informed your decisions are, you should explore this option.
  • How To Read and Understand a Histogram (Professional Photographer Magazine Web Exclusives) 23 January 2010 4:55 UTC www.ppmag.com [Source type: General]

.An interesting feature of this graph is that the number recorded for "at least 30 but less than 35 minutes" is higher than for the bands on either side.^ Most will agree that the digital camera can record a little more than transparency film, and a little less than negative film.
  • Understanding Your Digital Camera's Histogram - CleanImages.com 23 January 2010 4:55 UTC www.cleanimages.com [Source type: General]

^ Rather, inventive subject matter may lie in less than all features of a particular disclosed embodiment.
  • HISTOGRAM-BASED THORACIC IMPEDANCE MONITORING - Patent application 23 January 2010 4:55 UTC www.faqs.org [Source type: Reference]

^ In addition, you may notice the right hand side of the hills is higher than the left hand side most of the time.

This is likely to have arisen from people rounding their reported journey time. This rounding is a common phenomenon when collecting data from people.
.
Histogram of travel time, US 2000 census.
^ Most people are accustomed to seeing Travel data displayed with respect to Time.  A histogram displays data with respect to number of occurrences instead of Time.
  • Welcome To ShockClock - 6.2.3 Travel Histogram 23 January 2010 4:55 UTC new.racetech.com [Source type: Reference]

.Area under the curve equals the total number of cases.^ Fill area under fitted curve .
  • The UNIVARIATE Procedure : HISTOGRAM Statement 23 January 2010 4:55 UTC www.uc.edu [Source type: Reference]

^ The area under the curve represents the total number of cases (124 million).
  • Histogram encyclopedia topics | Reference.com 23 January 2010 4:55 UTC www.reference.com [Source type: Reference]

^ Compute the total area under the histogram.
  • contrib/gel/vifa: vifa_histogram Class Reference 23 January 2010 4:55 UTC www.lems.brown.edu [Source type: Reference]
  • contrib/gel/vifa: vifa_histogram Class Reference 23 January 2010 4:55 UTC public.kitware.com [Source type: Reference]

This diagram uses Q/width from the table.
Data by absolute numbers
Interval Width Quantity Quantity/width
0 5 4180 836
5 5 13687 2737
10 5 18618 3723
15 5 19634 3926
20 5 17981 3596
25 5 7190 1438
30 5 16369 3273
35 5 3212 642
40 5 4122 824
45 15 9200 613
60 30 6461 215
90 60 3435 57
.This histogram shows the number of cases per unit interval so that the height of each bar is equal to the proportion of total people in the survey who fall into that category.^ The total number of events in the first histogram is equal to: and in the second histogram.
  • TH1 23 January 2010 4:55 UTC root.cern.ch [Source type: Reference]

^ The function returns the total number of entries in the result histogram if the merge is successfull, -1 otherwise.
  • TH1 23 January 2010 4:55 UTC root.cern.ch [Source type: Reference]

^ In the case of a weighted histogram if the number of events is unknown, then we can apply this recommendation for the equivalent number of events as The minimal expected frequency for an unweighted histogram must be 1.
  • TH1 23 January 2010 4:55 UTC root.cern.ch [Source type: Reference]

.The area under the curve represents the total number of cases (124 million).^ The area under the curve represents the total number of cases (124 million).
  • Histogram encyclopedia topics | Reference.com 23 January 2010 4:55 UTC www.reference.com [Source type: Reference]

^ Compute the total area under the histogram.
  • contrib/gel/vifa: vifa_histogram Class Reference 23 January 2010 4:55 UTC www.lems.brown.edu [Source type: Reference]
  • contrib/gel/vifa: vifa_histogram Class Reference 23 January 2010 4:55 UTC public.kitware.com [Source type: Reference]

^ Total area under the histogram.
  • contrib/brl/bbas/bsta: bsta_histogram< T > Class Template Reference 23 January 2010 4:55 UTC www.lems.brown.edu [Source type: Reference]

.This type of histogram shows absolute numbers.^ The following table shows the parameters required for each of the three types of histograms, defined by their @Mode value: DateRange, DateMonths, and NumberRange.

^ For an 8-bit grayscale image a histogram may be determined that graphically displays 256 numbers showing the distribution of pixels amongst those grayscale values.
  • HISTOGRAM-MODELING BASED ALGORITHM FOR CONTRAST ENHANCEMENT - Patent application 23 January 2010 4:55 UTC www.faqs.org [Source type: Reference]

^ The histogram of an image is a graph showing the number of pixels in an image at each different intensity value found in that image.
  • HISTOGRAM-MODELING BASED ALGORITHM FOR CONTRAST ENHANCEMENT - Patent application 23 January 2010 4:55 UTC www.faqs.org [Source type: Reference]


.
Histogram of travel time, US 2000 census.
^ Most people are accustomed to seeing Travel data displayed with respect to Time.  A histogram displays data with respect to number of occurrences instead of Time.
  • Welcome To ShockClock - 6.2.3 Travel Histogram 23 January 2010 4:55 UTC new.racetech.com [Source type: Reference]

Area under the curve equals 1. This diagram uses Q/total/width from the table.
Data by proportion
Interval Width Quantity (Q) Q/total/width
0 5 4180 0.0067
5 5 13687 0.0221
10 5 18618 0.0300
15 5 19634 0.0316
20 5 17981 0.0290
25 5 7190 0.0116
30 5 16369 0.0264
35 5 3212 0.0052
40 5 4122 0.0066
45 15 9200 0.0049
60 30 6461 0.0017
90 60 3435 0.0005
.This histogram differs from the first only in the vertical scale.^ The top of the histogram (top of mountain peak) represents the number of different colors, a value you cannot control, so it is for your information only.
  • Understanding Your Digital Camera's Histogram - CleanImages.com 23 January 2010 4:55 UTC www.cleanimages.com [Source type: General]

^ The horizontal scale of the histogram measures exposure latitude, and the vertical scale measures quantity: it tells us how many pixels in the image have a specific luminosity value.
  • How To Read and Understand a Histogram (Professional Photographer Magazine Web Exclusives) 23 January 2010 4:55 UTC www.ppmag.com [Source type: General]

^ Normally, a histogram is scaled vertically so that whatever value has the most pixels reaches all the way to the top of the graph, and everything else is sized proportionately.
  • Ironic Sans: Idea: The Histogram as the Image 23 January 2010 4:55 UTC www.ironicsans.com [Source type: General]

.The height of each bar is the decimal percentage of the total that each category represents, and the total area of all the bars is equal to 1, the decimal equivalent of 100%.^ INHEIGHT= value specifies the height, in percentage screen units of text, to use inside the framed areas of the histogram.
  • The UNIVARIATE Procedure : HISTOGRAM Statement 23 January 2010 4:55 UTC www.uc.edu [Source type: Reference]

^ (A histogram, for those unfamiliar with the term, is a bar graph representing all the tones in an image — it typically looks something like a mountain range).
  • Ironic Sans: Idea: The Histogram as the Image 23 January 2010 4:55 UTC www.ironicsans.com [Source type: General]

^ The first value must be zero and the last value must be greater than or equal to the height of the largest bar.
  • The UNIVARIATE Procedure : HISTOGRAM Statement 23 January 2010 4:55 UTC www.uc.edu [Source type: Reference]

.The curve displayed is a simple density estimate.^ Request estimated density curve .
  • The UNIVARIATE Procedure : HISTOGRAM Statement 23 January 2010 4:55 UTC www.uc.edu [Source type: Reference]

^ FILL fills areas under the fitted density curve or the kernel density estimate with colors and patterns.
  • The UNIVARIATE Procedure : HISTOGRAM Statement 23 January 2010 4:55 UTC www.uc.edu [Source type: Reference]

^ BETA <( beta-suboptions )> displays a fitted beta density curve on the histogram.
  • The UNIVARIATE Procedure : HISTOGRAM Statement 23 January 2010 4:55 UTC www.uc.edu [Source type: Reference]

.This version shows proportions, and is also known as a unit area histogram.^ Most display modes on a digital camera's back LCD will have an option that shows a small preview of the photo alongside a small version of the histogram.
  • Using Your Camera’s Histogram to Take Better Digital Photographs | Psdtuts+ 23 January 2010 4:55 UTC psd.tutsplus.com [Source type: FILTERED WITH BAYES]


.In other words a histogram represents a frequency distribution by means of rectangles whose widths represent class intervals and whose areas are proportional to the corresponding frequencies.^ Image forming apparatus which performs gamma correction on the basis of a cumulative frequency distribution produced from a histogram of image data representing a selected area of an image .
  • Automatic tone correction of images using non-linear histogram processing (US5544258) 23 January 2010 4:55 UTC www.delphion.com [Source type: Academic]

^ EMPTY specifies the color for a horizontal bar whose length (relative to the width of the tile) indicates the proportion of the total frequency that is represented by the corresponding cell in a comparative histogram.
  • The UNIVARIATE Procedure : HISTOGRAM Statement 23 January 2010 4:55 UTC www.uc.edu [Source type: Reference]

^ Thoracic impedance-indicating signal characteristic values detected in the bins corresponding to the defined tail of the distribution represent evidence of fluid accumulation events.
  • HISTOGRAM-BASED THORACIC IMPEDANCE MONITORING - Patent application 23 January 2010 4:55 UTC www.faqs.org [Source type: Reference]

.The intervals are placed together in order to show that the data represented by the histogram while being exclusive is also continuous.^ Image forming apparatus which performs gamma correction on the basis of a cumulative frequency distribution produced from a histogram of image data representing a selected area of an image .
  • Automatic tone correction of images using non-linear histogram processing (US5544258) 23 January 2010 4:55 UTC www.delphion.com [Source type: Academic]

^ Since the data consist of the numbers 1, 2, 3, 4, 5, 6 and the starting point is 0.5, a width of one places the 1 in the middle of the interval from 0.5 to 1.5, the 2 in the middle of the interval from 1.5 to 2.5, the 3 in the middle of the interval from 2.5 to 3.5, the 4 in the middle of the interval from _______ to _______, the 5 in the middle of the interval from _______ to _______, and the _______ in the middle of the interval from _______ to _______ .
  • Descriptive Statistics: Histogram 23 January 2010 4:55 UTC cnx.org [Source type: General]

^ If the render function is to draw the histogram using lines, it simply joins the values together to form a continuous line.
  • Histogram 23 January 2010 4:55 UTC jscience.org [Source type: Reference]

.(E.g., in a histogram it is possible to have two connnecting intervals of 10.5-20.5 and 20.5-33.5, but not two connecting intervals of 10.5-20.5 and 22.5-32.5. Empty intervals are represented as empty and not skipped.^ So for example Histogram("sample", 2, 0.0, 20.0, aModel) contains two in-range bins and one bin for underflow and one for overflow.
  • Histogram (RepastJ API Documentation) 23 January 2010 4:55 UTC repast.sourceforge.net [Source type: Reference]

^ So for example Histogram("sample", 2, 0.0, 20.0) contains two in-range bins and one bin for underflow and one for overflow.
  • Histogram (RepastJ API Documentation) 23 January 2010 4:55 UTC repast.sourceforge.net [Source type: Reference]

^ Its boundaries are [Double.NEGATIVE_INFINITY,10.0), [10.0, 20.0), [20.0, 22.0), [22.0, Double.POSITIVE_INFINITY], the first and last bins being for underflow and overflow.
  • Histogram (RepastJ API Documentation) 23 January 2010 4:55 UTC repast.sourceforge.net [Source type: Reference]

)[4]

Activities and demonstrations

.The SOCR resource pages contain a number of hands-on interactive activities demonstrating the concept of a histogram, histogram construction and manipulation using Java applets and charts.^ Numpy Example List This page contains a large database of examples demonstrating most of the Numpy functionality.
  • Numpy Example List - 23 January 2010 4:55 UTC www.scipy.org [Source type: Reference]

^ Histogram extends java.lang.Object implements java.lang.Cloneable A Histogram is used to obtain a set of counts for a set of elements.
  • Histogram (Jive Integrated Server API (5.0.5) Developer Javadocs) 23 January 2010 4:55 UTC www.jivesoftware.com [Source type: FILTERED WITH BAYES]

^ Histogram (java.lang.String title, int numBins, double min, double max) Constructs a histogram with a fixed xaxis interval.
  • Histogram (RepastJ API Documentation) 23 January 2010 4:55 UTC repast.sourceforge.net [Source type: Reference]

Mathematical definition

.
An ordinary and a cumulative histogram of the same data.
^ The ordinary mechanism for saving the histogram records the raw data and the configuration to be used by this class.

The data shown is a random sample of 10,000 points from a normal distribution with a mean of 0 and a standard deviation of 1.
.In a more general mathematical sense, a histogram is a mapping mi that counts the number of observations that fall into various disjoint categories (known as bins), whereas the graph of a histogram is merely one way to represent a histogram.^ Bins The number of bins in this Histogram .
  • Histogram (RepastJ API Documentation) 23 January 2010 4:55 UTC repast.sourceforge.net [Source type: Reference]

^ One way to get that feedback is through the histogram.
  • Webshots Blog » Pro Tip: How To Use a Histogram 23 January 2010 4:55 UTC blog.webshots.com [Source type: General]

^ NumBins () Gets the number of bins in this histogram.

Thus, if we let n be the total number of observations and k be the total number of bins, the histogram mi meets the following conditions:
n = \sum_{i=1}^k{m_i}.

Cumulative histogram

.A cumulative histogram is a mapping that counts the cumulative number of observations in all of the bins up to the specified bin.^ Specify maximum number of bins to display .
  • The UNIVARIATE Procedure : HISTOGRAM Statement 23 January 2010 4:55 UTC www.uc.edu [Source type: Reference]

^ Bins The cumulative histogram bins.
  • Histogram 23 January 2010 4:55 UTC jscience.org [Source type: Reference]

^ Bins The number of bins in this Histogram .
  • Histogram (RepastJ API Documentation) 23 January 2010 4:55 UTC repast.sourceforge.net [Source type: Reference]

That is, the cumulative histogram Mi of a histogram mj is defined as:
M_i = \sum_{j=1}^i{m_j}.

Number of bins and width

.There is no "best" number of bins, and different bin sizes can reveal different features of the data.^ In Example 10, the system of Example 9 is optionally configured such that the deviation is indicative of a difference in the number of counts from the corresponding baseline histogram bin.
  • HISTOGRAM-BASED THORACIC IMPEDANCE MONITORING - Patent application 23 January 2010 4:55 UTC www.faqs.org [Source type: Reference]

^ If there are an odd # of elements numbered 1...2N+1, returns the bin containing element N. If there are an even number of elements, 1...2N, returns the bin containing element N (since we do not know a priori that the elements have an associated add operation, we can't necessarily average elements N and N+1 for the even size case).
  • Histogram (Jive Forums Professional 3.2.10 Documentation) 23 January 2010 4:55 UTC www.jivesoftware.com [Source type: FILTERED WITH BAYES]

^ If the data are discrete and there are not too many different values, a width that places the data values in the middle of the bar or class interval is the most convenient.
  • Descriptive Statistics: Histogram 23 January 2010 4:55 UTC cnx.org [Source type: General]

.Some theoreticians have attempted to determine an optimal number of bins, but these methods generally make strong assumptions about the shape of the distribution.^ The number of events in the ith bin is a random variable with a distribution approximated by a Poisson probability distribution for the first histogram and with distribution for the second histogram.
  • TH1 23 January 2010 4:55 UTC root.cern.ch [Source type: Reference]

^ By using MAXNBIN= to limit the number of bins, you can narrow the window about the data distribution in the key cell.
  • The UNIVARIATE Procedure : HISTOGRAM Statement 23 January 2010 4:55 UTC www.uc.edu [Source type: Reference]

^ If you choose too large bin size, the histogram can not represent the shape of the underlying distribution because the resolution isn't good enough.

.You should always experiment with bin widths before choosing one (or more) that illustrate the salient features in your data.^ Depending on your camera, you may or may not be able to do one or more of the above.
  • Digital Photography Tutorial: Histogram - Photoxels 23 January 2010 4:55 UTC www.photoxels.com [Source type: General]

^ Exactly what data is the histogram you see displayed on your camera’s LCD preview screen based on?
  • How To Read and Understand a Histogram (Professional Photographer Magazine Web Exclusives) 23 January 2010 4:55 UTC www.ppmag.com [Source type: General]

^ Some cameras can be "profiled" to capture light ranges more effectively in one direction or the other, but when you push one area, the opposite area must give.
  • Understanding Your Digital Camera's Histogram - CleanImages.com 23 January 2010 4:55 UTC www.cleanimages.com [Source type: General]

The number of bins k can be calculated directly, or from a suggested bin width h:
k = \left \lceil \frac{\max x - \min x}{h} \right \rceil.
The braces indicate the ceiling function.
Sturges' formula[5]
k = \lceil \log_2 n + 1 \rceil, \,
which implicitly bases the bin sizes on the range of the data, and can perform poorly if n < 30.
Scott's choice[6]
h = \frac{3.5 \sigma}{n^{1/3}},
where .σ is the sample standard deviation.^ Value returned is standard deviation of sample standard deviation.
  • TH1 23 January 2010 4:55 UTC root.cern.ch [Source type: Reference]

Square-Root Choice
k = \sqrt{n},
which takes the square root of the number of data points in the sample (used by Excel histograms and many others)
Freedman–Diaconis' choice[7]
h = 2 \frac{\operatorname{IQR}(x)}{n^{1/3}},
which is based on the interquartile range. A good discussion of this and other rules for choice of bin widths is in [8]

See also

References

  1. ^ Howitt, D. and Cramer, D. (2008) "Statistics in Psychology". Prentice Hall
  2. ^ Nancy R. Tague (2004). "Seven Basic Quality Tools". The Quality Toolbox. Milwaukee, Wisconsin: American Society for Quality. p. 15. http://www.asq.org/learn-about-quality/seven-basic-quality-tools/overview/overview.html. Retrieved 2010-02-05. 
  3. ^ M. Eileen Magnello (December 1856). "Karl Pearson and the Origins of Modern Statistics: An Elastician becomes a Statistician". The New Zealand Journal for the History and Philosophy of Science and Technology 1 volume. ISSN 1177–1380. http://www.rutherfordjournal.org/article010107.html. 
  4. ^ Dean, S., & Illowsky, B. (2009, February 19). Descriptive Statistics: Histogram. Retrieved from the Connexions Web site: http://cnx.org/content/m16298/1.11/
  5. ^ Sturges, H. A. (1926). "The choice of a class interval". J. American Statistical Association: 65–66. 
  6. ^ Scott, David W. (1979). "On optimal and data-based histograms". Biometrika 66 (3): 605–610. doi:10.1093/biomet/66.3.605. 
  7. ^ Freedman, David; Diaconis, P. (1981). "On the histogram as a density estimator: L2 theory". Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete 57 (4): 453–476. doi:10.1007/BF01025868. 
  8. ^ W. N. Venables and B. D. Ripley: "Modern Applied Statistics with S", Springer, in (4thedition) section 5.6: "Density Estimation"

Further reading

  • Lancaster, H.O. An Introduction to Medical Statistics. John Wiley and Sons. 1974. ISBN 0 471 51250-8

External links


Simple English

[[File:|thumbnail|right|Example of a histogram of 100 normally distributed random values.]]A histogram is a concept from statistics. It is a graphical display that tells about the distribution of the samples involved. It is basically the graphical display of a table with many categories. The table tells for each category how many samples there are in it. The word histogram is derived from histos and gramma in Greek. Histos means web or mast. Gramma means drawing, record or writing. A histogram of something is therefore , etymologically speaking, a drawing of the web of this something.

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 smooth Probability density function from the supplied data.



Citable sentences

Up to date as of December 21, 2010

Here are sentences from other pages on Histogram, which are similar to those in the above article.








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