How do you describe the distribution in a data statistically? For example, describe the distribution of the variable "heights of students,"...

There are 3 of variables given: height, belly button
height and foot length.

We explain distribution in respect
of the variable height. You can apply the same idea to the other two variables. Here we
take the height of the students of a college . The characteristic height is varying from
student to student.By statistical distribution we mean showing the extent of variation
of the height by a diagram or a curve or a graph. The pattern by which the graph 
 look may be a bell shaped normal cuve, or a curve whose peak is shifted to left or
right or else a stright line etc to say a few types.

We
also try to understand the extentent of distribution of heights of students by certain
parameters like mean, median, range , standardard deviation or
variance.

Mean:

Let us take
the variable the heights of students. If  there are  n students in a college,  and their
heights are x1, x2, x3,......xn, then the mean height  x bar is goven
by:

x bar =  
(x1++x2+x3+x4+.....+xn)/n

Let xl  and xt be the lowest
tallest  among.

Range:

 the
heights, x1,x2,x3,...xn of the students. Then the range R of the varible  height  is
given by:

R = xt -
xl.

Median:

If the students
are arranged according to their heights, then the height of the middle student in the
order is the median. If there happens to be two middle students(in case of even number
of students) then the heights of those two students  are added and divided by two to get
the median height of the
students.

Variance:

The variance
 v is average of the sum of the squared deviations from the mean and is given
by:

v =  summation (xi- xbar)^2/ n , i = 1 to
n.

Standard deviation:

The
standard deviation  sigma or s is the square root of variance
.

s = sqrt { summation (xi-xbar)^2/n  , i = 1 to n.
}.

Hope this may help.