Arithmetic mean (AM)
The arithmetic
mean is the
"standard" average, often simply called the "mean".
(Our solved example in mathguru.com uses this concept).
The mean may often be confused with the median, mode or
range. The mean is the arithmetic average of a set of values, or distribution;
however, for skewed distributions, the mean is not
necessarily the same as the middle value (median), or the most likely (mode).
For example, mean income is skewed upwards by a small number of people with
very large incomes, so that the majority has an income lower than the mean. By
contrast, the median income is the level at which half the population is below
and half is above. The mode income is the most likely income, and favors the
larger number of people with lower incomes. The median or mode are often more
intuitive measures of such data.
Nevertheless, many skewed distributions are best described by
their mean - such as the exponential and Poisson
distributions.
For example, the arithmetic mean of six values: 34, 27, 45, 55,
22, 34 is
http://en.wikipedia.org/wiki/Mean
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. (Our solved example in
mathguru.com uses this concept)
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
Mode (statistics)
In statistics, the mode is the value that occurs most
frequently in a data set or a probability
distribution. (Our solved example in mathguru.com uses
this concept)
In some fields, notably education, sample data are often called scores, and the sample mode is
known as the modal score.
Like the statistical mean and the median, the mode is a way of capturing important information about a random variable or a population in a single quantity. The mode is in
general different from the mean and median, and may be very different for
strongly skewed distributions.
The mode is not necessarily unique, since the same maximum
frequency may be attained at different values. The most ambiguous case occurs
in uniform distributions, wherein
all values are equally likely.
http://en.wikipedia.org/wiki/Mode_(statistics)
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.