Finding a Mean in a Survey

Date: 03/13/2002 at 10:59:12
From: Lisa Albuquerque
Subject: Figuring out a mean from a group of numbers

I am working on a survey project and have to figure out how to get a 
mean from a group of numbers after extracting a certain group of 
survey respondents. The responses were Slightly Disagree, Disagree, 
Neutral, Agree, Strongly Agree, and Don't Know. 
 
It seems as if if I assigned a numerical value to each of the 
categories and then did something magical I could come up with the 
mean response. I've done percentages of the total, assigned values, 
and turned Excel inside out for clues, and am getting more confused by 
the minute. Please tell me how to fix this!  

Thanks,
Lisa Albuquerque

Date: 03/13/2002 at 12:13:01
From: Doctor Ian
Subject: Re: Figuring out a mean from a group of numbers

Hi Lisa,

You might assign the following quantities to the responses:

  -2    Strongly disagree
  -1    Disagree
   0    Neutral
   1    Agree
   2    Strongly agree

Next, you would add up all the responses, and divide by the number of 
responses, e.g., 

         -2 + -2 + -1 + 0 + 0 + 0 + 1 + 1 + 2 + 2 + 2 + 2
  mean = ------------------------------------------------
                             12

If you were doing it by hand, you could simply cancel out some of the 
pairs, 

          +---------------------------------------------+
          |    +------------------------------------+   |
          |    |    +-------------------+           |   |
          |    |    |                   |           |   |
         -2 + -2 + -1 + 0 + 0 + 0 + 1 + 1 + 2 + 2 + 2 + 2
  mean = ------------------------------------------------
                             12


         0 + 0 + 0 + 1 + 2 + 2 
  mean = ---------------------- = 5/12
                  12

Note that this does _not_ affect the denominator!

Note that you could assign the values 1 to 5 instead of the values -2 
to 2, and it would work the same way (except you could no longer use 
cancellation). The advantage of the zero-centered scale is that it's 
easier to tell at a glance what a particular value _means_. It's much 
easier to interpret a diagram like 


       Disagree <--------+--------> Agree
                     #### 
                      ###
                          ########
                          ##
                 ########
                   ######
                          ####

than a diagram like 

         Disagree +--------------------+ Agree
                   ####
                   ##
                   ##############
                   ###################
                   ############
                   #####
                   ###################
 
Choosing the right notation is often half the battle.

Does this help? 

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

Date: 03/13/2002 at 14:30:22
From: Lisa Albuquerque
Subject: Figuring out a mean from a group of numbers

Dr. Ian - 

Thanks so much for your response. I followed your weighting suggestion 
and got the answers I need.  Thanks so much for the very quick 
response! 

Lisa