Frequency Table

Date: 10/13/2003 at 10:26:18
From: Del 
Subject: Frequency table

Hello Dr. Math,

My child has been asked to create a frequency table using the values

  7, 2, 6, 7, 6, 5, 4, 2, 5, 1, 0, 2, 5 

But I'm stumped because I'm not sure what one is (what it looks like)
or how I might create one.  

Date: 10/15/2003 at 11:21:23
From: Doctor Luis
Subject: Re: Frequency table

Hi Del,

Frequency means just that: How many times a given element repeats.

It's easier to make a frequency table if we arrange the elements in
ascending order:

  0, 1, 2, 2, 2, 4, 5, 5, 5, 6, 6, 7, 7
                    
Next, we count the number of times that each element occurs.  For
example, 5 occurs 3 times:

  0, 1, 2, 2, 2, 4, 5, 5, 5, 6, 6, 7, 7, 
                    -------

So that count becomes the 'frequency' for 5 in the table:

  n | x_n | f_n 
 ---|-----|-----
  1 |  0  |    
  2 |  1  |    
  3 |  2  |    
  4 |  4  |   
  5 |  5  |  3  
  6 |  6  |    
  7 |  7  |    

Filling in the rest of the table, we get

  n | x_n | f_n 
 ---|-----|-----
  1 |  0  |  1  
  2 |  1  |  1  
  3 |  2  |  3  
  4 |  4  |  1 
  5 |  5  |  3  
  6 |  6  |  2  
  7 |  7  |  2  

Note that the frequencies add up to 13, which is the number of
elements we started with (counting the repetitions of course).  Do you
see why this should be the case? 

I hope this helped!  Let us know if you have any more questions.

- Doctor Luis, The Math Forum
  http://mathforum.org/dr.math/