normal or gaussian distribution 
mean (m) : in probability
and statistics, the expected value (mathematical expectation) of a random
variable, the limiting value to which the sample mean converges as the
sample size is increased indefinitely (if the limit exists)

population mean : the mean of the probability distribution characterizing
a specified population; for a finite population, the arithmetic mean of
the population values

arithmetic mean : the sum of n
numbers divided by n. m = lim_{n=>+oo}[sum(x_{i})/N]

geometric mean : the nth root
of the product of n numbers, e.g., the geometric mean of [2,8,32]
is (2 x 8 x 32)^{1/3} = 8.

harmonic mean (m)
: reciprocal of the mean of the reciprocals of the individual values in
a given set; e.g., for the set [10, 40, 60] the harmonic mean is 1 / [
1/3 ( 1/10 + 1/40 + 1/60 )] = 21.2.

average absolute difference
= 1/n ^{.} summation(x_{i}x^{})
coefficient of variation
(CV) : the standard deviation divided by the mean, sometimes multiplied
by 100; a unitless quantity indicating the variability around the mean
in relation to the size of the mean
deviance / average quadratic difference =
1/n ^{.} summation[(x_{i}x^{})^{2}]
variance (s^{2})
= 1/(n1) ^{.} sum(x_{i}x^{})^{2}
: in statistics, a measure of the variation shown by a set of observations:
the average of the squared deviations from the mean; it is the square of
the standard deviation

s^{2}(x+a) = s^{2}
(x)

s^{2}(bx) = b^{2}s^{2}(x)
=> s^{2}(a+bx) = b^{2}s^{2}(x)
range : an interval in which values sampled
from a population, or the values in the population itself, are known to
lie = x_{max}  x_{min}
population standard deviation
(SD / s) = [1/(n1) ^{.} summation(x_{i}x^{})^{2}]^{1/2}
: in statistics a measure of the amount by which each value deviates
from the mean; equal to the square root of the variance, i.e., the square
root of the average of the squared deviations from the mean. It is the
most commonly used measure of dispersion of statistical data

skewness of a probability distribution, lack
of symmetry about the mean, or any measure of the lack of symmetry = [summation(x_{i}x^{})^{2}]/ns^{2}

> 0 : right tail

= 0 : symmetrical

< 0 : left tail
kurtosis : the degree of peakedness or flatness
of a probability distribution, relative to the normal distribution with
the same variance = [sum (x_{i}x^{})^{2}]/ns^{4}

< 3 : leptokurtic : pertaining to a probability distribution
more heavily concentrated around the mean, i.e., having a sharper, narrower
peak, than the normal distribution with the same variance

= 3 : normal distribution

> 3 : platykurtic : pertaining to a probability distribution less
concentrated about the mean, i.e., having a broader, flatter peak than
the normal distribution with the same variance

skew distribution : a frequency distribution that is asymmetric.

mode : the most frequently occurring value or
item in a distribution; when data are grouped, it is the midpoint of the
grouping with the highest frequency. A distribution with 2 peaks is bimodal
median (M_{e}) : any value that
divides the probability distribution of a random variable in half, i.e.,
the probability of observing a value above the median and the probability
of observing a value below the median are both less than or equal to one
half. For a finite population or sample, the median is

the middle value of an odd number of values (arranged in ascending order)

any value between the 2 middle values of an even number of values; in the
latter case it is conventional to use the average of the 2 middle values
The median is the value for which the sum of x_{i}  M_{e}
is minimal. Its value doesn't change when values of x < M_{e}
or x > M_{e} are changed and can be used also for ordinal
continuous variables. 
quantile : any of the values that divide
the range of an observed or theoretical probability distribution into a
given number of equal, ordered parts. Each value divides the range into
2 specified parts, with the part below the value corresponding to a prescribed
fraction p and the part above to 1  p.

percentile : any one of the 99 values that
divide the range of a probability distribution or sample into 100 intervals
of equal probability or frequency, e.g., 45% of a population scores below
the 45th percentile

quartile : any of the 3 values that divide
the range of a probability distribution into 4 parts of equal probability;
i.e., the 1st (Q_{1}), 2nd (Q_{2}), and 3rd (Q_{3})
quartiles are the 25th, 50th, and 75th percentiles.

quintile : any of the 5 values that divide
the range of a probability distribution into 5 parts of equal probability,
i.e., the 1st, 2nd, 3rd, and 4th quintiles are the 20th, 40th, 60th, and
80th percentiles
interquartile range : the difference
between the data values at the 75th and 25th percentiles (Q_{3 }
Q_{1}), encompassing the middle 50 percent of the data

