Histogram
A method for representing experimental data. A histogram is constructed as follows. The entire range of the observed values of some random variable
is subdivided into
grouping intervals (which are usually all of equal length) by points
; the number of observations
per interval
and the frequency
are computed. The points
are marked on the abscissa, and the segments
(
) are taken as the bases of rectangles with heights
. If the intervals
have equal lengths, the altitudes of the rectangles are taken as
or as
. Thus, let the measurements of trunks of 1000 firs give the following results:'
<tbody> </tbody>
|
The histogram for this example is shown in the figure. diameter in cm. number of trunks
Figure: h047450a
Comments
The histogram can be considered as a technique of density estimation (cf. also Density of a probability distribution), and there is much literature on its properties as a statistical estimator of an unknown probability density as and the grouping intervals are made smaller (grouping intervals of lengths
seem optimal).
References
[a1] | D. Freedman, P. Diaconis, "On the histogram as a density estimator: ![]() |
Histogram. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Histogram&oldid=12918