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  
A histogram is a representation of a frequency distribution by using rectangles. The width of the rectangle (x-axis) represents  
different values included into one class whereas the height specifies the number of elements that belong into this class (divided by the number of different values in each class). The size of an area of each column (not its height) specifies how many data-elements of each class occur in the total data set. 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 cameras.
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.


= Example =
= Example =


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. Frequenzy values (second column) according to the classes are 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.
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 results for each class are 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.


<table style="height:16px" border="0">
<table style="height:16px" border="0">

Revision as of 11:42, 8 November 2007

Definitions

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). The categories are usually specified as non-overlapping intervals of some variable. The categories (bars) must be adjacent.
[Wikipedia, 2007]


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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

A histogram is a representation of a frequency distribution by using rectangles. The width of the rectangle (x-axis) represents 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.

Example

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 results for each class are 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

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References

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