Explanation:
Median
In probability theory and statistics,
a median is described as the numerical value
separating the higher half of a sample, a population,
or a probability distribution,
from the lower half. The median of
a finite list of numbers can be found by arranging all the observations from
lowest value to highest value and picking the middle one. If there is an even
number of observations, then there is no single middle value; the median is
then usually defined to be the mean of the two middle values.
In a sample of data, or a finite population, there may be no
member of the sample whose value is identical to the median (in the case of an
even sample size), and, if there is such a member, there may be more than one
so that the median may not uniquely identify a sample member. Nonetheless, the
value of the median is uniquely determined with the usual definition. A related
concept, in which the outcome is forced to correspond to a member of the
sample, is the medoid.
At most, half the population has values less than the median, and, at most, half have
values greater than the median. If both groups contain less than half the
population, then some of the population is exactly equal to the median. For
example, if a < b < c,
then the median of the list {a, b, c} is b, and, if a < b < c < d,
then the median of the list {a, b, c, d}
is the mean of b and c;
i.e., it is (b + c)/2.
http://en.wikipedia.org/wiki/Median
In mathematics and statistics,
the arithmetic mean, often referred to as simply the mean or average when
the context is clear, is a method to derive the central tendency of a sample
space. The term "arithmetic mean" is preferred in mathematics and
statistics because it helps distinguish it from other means such as
the geometric and harmonic
mean.
Definition
Suppose we have sample space . Then the arithmetic mean A is defined via the
equation
.
In statistics,
the absolute deviation of an
element of a data set is the absolute
difference between that element and a given point. Typically
the point from which the deviation is measured is a measure of central
tendency, most often the median or
sometimes the mean of the
data set.
D_{i} =
| x_{i} − m(X) |
where
D_{i} is the absolute deviation,
x_{i} is the data element
and m(X) is the chosen measure of central
tendency of the data set-sometimes the mean (), but most often the median.
Average
absolute deviation
The average
absolute deviation, or simply average deviation of a data set is the average of the absolute deviations and is a summary statistic of statistical
dispersion or variability. It is
also called the mean absolute
deviation, but this is easily
confused with the median absolute
deviation.
The average absolute deviation of a set {x_{1}, x_{2}, ..., x_{n}} is
Mean
absolute deviation
The mean
absolute deviation (MAD) is
the mean absolute deviation from the mean. A related quantity, the mean absolute error (MAE), is a common measure of forecast error in time
series analysis, where this measures the average absolute deviation of
observations from their forecasts.
Although the term mean deviation is used as a synonym for mean absolute
deviation, to be precise it is not the same; in its strict interpretation
(namely, omitting the absolute value operation), the mean deviation of any data
set from its mean is always zero.
(Our solved example in mathguru.com uses this concept)
http://en.wikipedia.org/wiki/Absolute_deviation
Median absolute deviation
In statistics,
the median absolute deviation (MAD) is a robust measure
of the variability of a univariate sample
of quantitative data. It can also refer to the population parameter that is
estimated by the MAD calculated from a sample.
For a univariate data set X_{1}, X_{2}, ..., X_{n},
the MAD is defined as the median of the absolute
deviations from the data's median:
that is, starting with the residuals (deviations)
from the data's median, the MAD is the median of
their absolute values.
http://en.wikipedia.org/wiki/Median_absolute_deviation
The above explanation is copied from
Wikipedia, the free encyclopedia and is remixed as allowed under the Creative Commons
Attribution- ShareAlike 3.0 Unported License.