Statistics – Frequency Distribution
Frequency distribution is a table that displays the frequency of
various outcomes in a sample. Each entry in the table contains
the frequency or count of the occurrences of values within a
particular group or interval, and in this way, the table
summarizes the distribution of values in the sample.
Example
Problem Statement:
Constructing a frequency distribution table of a survey was taken
on Maple Avenue. In each of 20 homes, people were asked how many
cars were registered to their households. The results were
recorded as follows:
1  2  1  0  3  4  0  1  1  1  2  2  3  2  3  2  1  4  0  0 
Solution:
Steps to be followed for present this data in a frequency
distribution table.

Divide the results (x) into intervals, and then count the
number of results in each interval. In this case, the
intervals would be the number of households with no car (0),
one car (1), two cars (2) and so forth. 
Make a table with separate columns for the interval numbers
(the number of cars per household), the tallied results, and
the frequency of results in each interval. Label these
columns Number of cars, Tally and Frequency. 
Read the list of data from left to right and place a tally
mark in the appropriate row. For example, the first result is
a 1, so place a tally mark in the row beside where 1 appears
in the interval column (Number of cars). The next result is a
2, so place a tally mark in the row beside the 2, and so on.
When you reach your fifth tally mark, draw a tally line
through the preceding four marks to make your final frequency
calculations easier to read. 
Add up the number of tally marks in each row and record them
in the final column entitled Frequency.
Your frequency distribution table for this exercise should look
like this:
Frequency table for the number of cars registered in each household 


Number of cars (x)  Tally  Frequency (f) 
0  ${lvertlvertlvertlvert}$  4 
1  ${require{cancel} cancel{lvertlvertlvertlvert} lvert}$  6 
2  ${cancel{lvertlvertlvertlvert}}$  5 
3  ${lvertlvertlvert}$  3 
4  ${lvertlvert}$  3 
By looking at this frequency distribution table quickly, we can
see that out of 20 households surveyed, 4 households had no cars,
6 households had 1 car.
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