How do you describe the distribution in a data statistically?

For example, describe the distribution of the variable "heights of students," "belly button heights," "foot length."

Refer to the range, mean, median, mode, standard deviation and variance.

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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.

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