It seems to me you would have to proceed on a per question basis. While Darcy and random's answer of dividing by the number of responses given by a respondent would be what you would want to do if you were asking about amount of time spent on the bus, your question asked "What do you typically use the bus for?"

This question does not care if someone rides the bus twice a month, once for work and once for school, or if they ride it to school in the morning and work in the afternoon every single day. So dividing to try to normalize data here would not get you useful information because the question was not asking about a quantity.

In this case, if you have few enough answers, a venn diagram would be an ideal way to present this information. Lets say that A = work B = school and C = shopping. The data that you want to show is the number of people in the group A, B and C as well as the people in the intersection of AB, BC, AC and ABC. If you have more than 3 a venn diagram is no longer the best way to present the data, but you should still be interested in the sets of people who are in A, B, C, D... and the intersection of those sets. (Intersections being the people who are in both A and B because they answered they typically use it for work and school)

You will find that later on when you are trying to draw conclusions based on this data that having this breakdown will be more useful than having a breakdown where the sets were normalized by dividing out the multiple answers.

Someone who typically uses the bus for work should be fully counted, for example, when trying to draw conclusions about if workplace reimbursement for bus passes helps increase ridership. They should also be fully counted for drawing conclusions about the benefits to merchants at the mall if they also use the bus for shopping. These two things are not in any way exclusive. Almost all people who shop, work. It would not make sense to try to normalize this.

However, if you did want to normalize it, lets say you had groups A, B and C (A being all people who answered work, even if they also answered school, be being people who answered school even if they also answered work...) and the subsets AB, AC, BC, ABC (people who gave more than one answer) and you want to normalize the A group. The equation would be this:
A - (AB + AC) + ABC + (AC - ABC)/2 + (AB - ABC)/2 + ABC/3

If you are using a program like SPSS to do your computations, it can do stuff like this automatically. Otherwise it would be fairly easy to set up an Excel document to do it for you as well.
Source(s):
Oregon State Stats 314 and Math 231 :P


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