How to represent categorical data in a pie graph form?

Question

I have been asked to produce a pie graph of some categorical data.

On a simple scale it look like this:

House 1: Speak a foreign language , own a computer
House 2: Only lived in by women
House 3: Only lived in by women, speak a foreign language
House 4: Has pets
House 5: Has pets, own a computer
House 6: Speak a foreign language.

They want a pie graph that shows what percent of the different categories are represented.

Well if I go:
Speak a foreign language  = 3/6
Own a computer = 2/6
Only lived in by women = 2/6
has pets = 2/6

This totals 9/6 (i.e more than 100%)

Should I be totalling how many individual items there are and then creating my %'ages from that

i.e

Speak a foreign language  = 3/9
Own a computer = 2/9
Only lived in by women = 2/9
has pets = 2/9

this makes 100% but i am unsure if this is how you would do it so all the data is shown in one pie graph.

Answer 1

A pie chart - if it's suitable at all - is only suitable for mutually exclusive categories, since it represents a division of a whole into mutually exclusive subsets.

So, don't use a pie chart for categories that are not mutually exclusive. You're misleading people by doing so. (Why would you want to actively - and seemingly deliberately - mislead people about the information you're presenting?)

If you know the overlap in subsets, you might be able to use area to represent proportion, with overlapping area representing the intersection of the categories, but it won't look like a pie.

Alternatively, if possible, use the information you have to break the data into mutually exclusive subsets, which can then be represented as a pie chart. (Where possible, arrange those subsets so adjacent subsets combine to give other meaningful subsets)

This 'break into mutually exclusive subsets' and 'represent as a pie chart' will generally be less informative than other choices that represent all available combinations (think along the lines of a Venn-diagram, but with area also representing probability).