Explanation:
Assumed mean
In statistics the assumed mean is a method
for calculating the arithmetic mean and standard
deviation of a data set. It simplifies calculating accurate
values by hand. Its interest today is chiefly historical but it can be used to
quickly estimate these statistics. There are
other rapid calculation methods which are more
suited for computers which also ensure more accurate results than the obvious
methods.
Method
The method depends on estimating the mean and
rounding to an easy value to calculate with. This value is then subtracted from
all the sample values. When the samples are classed into equal size ranges a
central class is chosen and the count of ranges from that is used in the
calculations. For example for people's heights a value of 1.75m might be used
as the assumed mean.
For a data set with assumed mean x_{0} suppose:
Then
or for a sample standard deviation using Bessel's
correction:
(Our solved example in mathguru.com uses
this concept)
http://en.wikipedia.org/wiki/Assumed_mean
Variance
In probability
theory and statistics,
the variance is used as a
measure of how far a set of numbers are spread out from each other. It is one
of several descriptors of a probability distribution,
describing how far the numbers lie from the mean (expected
value). (Our solved example in
mathguru.com uses this concept)
In particular, the variance is one of the moments of a
distribution. In that context, it forms part of a systematic approach to
distinguishing between probability distributions. While other such approaches
have been developed, those based on moments are
advantageous in terms of mathematical and computational simplicity.
The variance is a parameter describing in
part either the actual probability distribution of an observed population of
numbers, or the theoretical probability distribution of a not-fully-observed
population of numbers. In the latter case a sample of data from such a
distribution can be used to construct an estimate of its variance: in the
simplest cases this estimate can be the sample variance.
http://en.wikipedia.org/wiki/Variance
Standard
deviation
Standard deviation is a widely used measurement of variability or
diversity used in statistics and probability
theory. It shows how much variation or "dispersion" there is from the
average (mean, or expected value). A low standard deviation indicates that the
data points tend to be very close to the mean, whereas
high standard deviation indicates that the data are spread out over a large
range of values.
Technically, the standard deviation of a statistical
population, data set, or probability
distribution is the square root of its
variance. It is algebraically simpler
though practically less robust than the average
absolute deviation. A useful
property of standard deviation is that, unlike variance, it
is expressed in the same units as the data. (Our solved example in mathguru.com uses this concept)
http://en.wikipedia.org/wiki/Standard_deviation
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