Mean frequency distribution

What is frequency distribution:
Frequency distribution is a term associated with statistics. In statistics, when we study some characteristic of a sample and then group the observations under various groups, a frequency distribution comes to play. A frequency distribution is a table showing the values of one or more variables and their respective frequencies of a given sample.

How to construct a frequency distribution:
In a univariate data, (univariate means that there is only one variable that we are interested in studying, the other factors are assumed to be constants) if x1,x2,x3,….xn are the possible values of the variable and f1,f2,f3,….fn are the frequencies with which each of the variables occur respectively. Then a table drawn as follows:
Variable (xi) Frequency (fi)
x1 f1
x2 f2
x3 f3
: :
: :
: :
xn fn
Is called a frequency distribution table of the data. Here i = 1,2,3,…..n. That means that the variable x can have n possible values and the frequency of each of the values are f. The above is a frequency distribution when the variable in question is discrete. For a continuous variable, the frequency distribution would look like this:
Class interval Frequency (fi)
C1 – C2 f1
C2 – C3 f2
C3 – C4 f3
: :
: :
: :
Cn-1 - Cn fn
Here, C1 – C2, C2 – C3 etc are the class intervals and f1,f2,f3… etc are the frequencies of the respective classes. The above distribution can be converted to a mean frequency distribution by replacing the class intervals with the respective class means.  We would need to do that to be able to easily work with the data. Its not exactly possible to calculate sample mean, sample standard deviations etc from a distribution having only class intervals. Therefore the mean frequency distribution would look like this:
Class interval Class mean Frequency (fi)
C1 – C2 (x1) ̅ f1
C2 – C3 (x2) ̅ f2
C3 – C4 (x3) ̅ f3
: : :
: : :
: : :
Cn-1 - Cn (xn) ̅ fn
Here, (x1,) ̅  (x2,) ̅  (x3,) ̅ …. (xn) ̅ etc are the respective class means.
The type of frequency distribution that we would construct would depend upon the frequency distribution example given to us. As we saw above, for a single variable, the distribution would be different if the variable is discrete and different if the variable is random. Similarly for more than one variables also the distributions would be different.