Teaching:TUW - UE InfoVis WS 2007/08 - Gruppe 07 - Aufgabe 1 - Histogram: Difference between revisions

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= Explanation =
= Explanation =


A histogram is a representation of a frequency distribution by using rectangles. The width of the rectangle (x-axis) represents
For drawing the histogram, the numerical values are first put in ascending order. Then the data field is split into j classes.     
different values included into one class whereas the area of each column (not it's height) specifies how many data-elements of each class occur in the total data set (absolute frequency). Histograms are widely being used in statistics but we can also find them in practical appliances in our everyday life as well, e.g. digital photography.
Each class has a defined width (class interval) - normally it is 1, but in special cases it is useful to choose a width > 1 - e.g. for displaying frequencies concerning distinct age groups. Under "Examples" we consider a histogram of varying class intervals.


= Example =
= Example =
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= Related Links =
= Related Links =
*[[wikipedia:Histogram|Wikipedia]]
 
*[http://en.wikipedia.org/wiki/Histogram]''Histogram'']
*[http://en.wikipedia.org/wiki/Histogram ''Definition of Histogram on Wikipedia'']  
*[http://www.luminous-landscape.com/tutorials/understanding-series/understanding-histograms.shtml ''Understanding Histograms in digital photography'']  
*[http://www.luminous-landscape.com/tutorials/understanding-series/understanding-histograms.shtml ''Understanding Histograms in digital photography'']  
*[http://www.shodor.org/interactivate/activities/histogram/ ''Histogram applet'']
*[http://www.shodor.org/interactivate/activities/histogram/ ''Histogram applet'']
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*[Lancaster, 1974] H.O. Lancaster,  An Introduction to Medical Statistics. John Wiley and Sons. 1974. ISBN 0 471 51250-8
*[Lancaster, 1974] H.O. Lancaster,  An Introduction to Medical Statistics. John Wiley and Sons. 1974. ISBN 0 471 51250-8
*[Wikipedia, 2007] Wikipedia, Histogram. Retrieved at: November 01, 2007. http://en.wikipedia.org/wiki/Histogram
*[Wallgreen et al., 1996] Anders Wallgreen, Britt Wallgreen, Rolf Persson, Ulf Jorner and Jan-Aage Haaland. Graphing Statistics & Data: Creating Better Charts. SAGE Publications, Thousand Oaks, London, New Delhi, 1996.
*[Wallgreen et al., 1996] Anders Wallgreen, Britt Wallgreen, Rolf Persson, Ulf Jorner and Jan-Aage Haaland. Graphing Statistics & Data: Creating Better Charts. SAGE Publications, Thousand Oaks, London, New Delhi, 1996.
*[Evans, 2004] Geraint Evans, Histograms. [http://www.censusatschool.ntu.ac.uk/ ''CensusAtScool'']. Retrieved at: November 08, 2007. http://www.censusatschool.ntu.ac.uk/files/histogram.pdf
*[Evans, 2004] Geraint Evans, Histograms. [http://www.censusatschool.ntu.ac.uk/ ''CensusAtScool'']. Retrieved at: November 08, 2007. http://www.censusatschool.ntu.ac.uk/files/histogram.pdf

Latest revision as of 19:19, 1 December 2007

Definitions[edit]

In statistics, a histogram is a graphical display of tabulated frequencies. A histogram is the graphical version of a table that shows what proportion of cases fall into each of several or many specified categories. The 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]


A histogram is used when we want to show frequencies of a continous variable. The continous variable can, of course, assume all values within an interval and the histogram reflects this by covering the whole of the interval concerned.
[Wallgreen et al., 1996]


Explanation[edit]

For drawing the histogram, the numerical values are first put in ascending order. Then the data field is split into j classes. Each class has a defined width (class interval) - normally it is 1, but in special cases it is useful to choose a width > 1 - e.g. for displaying frequencies concerning distinct age groups. Under "Examples" we consider a histogram of varying class intervals.

Example[edit]

As an example we consider values given from the table below to create a histogram (right image). The data derived from the first column of the table shows the class affiliation. According to the table values these classes are aligned along the x-axis of the histogram. The heigth of each histogram bar (frequency density) can be obtained by dividing the absolute frequenzy values (second column) by the corresponding class intervals. The resulting value of each class is then printed along the y-axis of the histogram. Once this is properly done, the histogram shows the amount of frequency according to any of the classes. Hence the histogram is a powerful visualisation that can make information accessable in just a few seconds, considering that the table on the left side is representing the same information, it is easy to understand the power of graphical visualisation.

Frequency density (height of a column) = n j / w j
Frequency (area) = Width x Height

class j absolute frequency nj class interval w j
1 (=> 24 ≤ x ≤ 26 ) 36 3
2 (=> 26 < x ≤ 28 ) 37 2
3 (=> 28 < x ≤ 33 ) 17 5
Histogram Illustration

Related Links[edit]

References[edit]

  • [Lancaster, 1974] H.O. Lancaster, An Introduction to Medical Statistics. John Wiley and Sons. 1974. ISBN 0 471 51250-8
  • [Wallgreen et al., 1996] Anders Wallgreen, Britt Wallgreen, Rolf Persson, Ulf Jorner and Jan-Aage Haaland. Graphing Statistics & Data: Creating Better Charts. SAGE Publications, Thousand Oaks, London, New Delhi, 1996.
  • [Evans, 2004] Geraint Evans, Histograms. CensusAtScool. Retrieved at: November 08, 2007. http://www.censusatschool.ntu.ac.uk/files/histogram.pdf
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