Tuesday, September 14, 2010

What is the meaningfulness of the gap between mean and median household income?

Torontoist's ward profiles include both mean ("average") and median household income for each ward. In some wards the mean and median are very close, and in others there's a huge gap. This is intriguing, but I can't figure out why it's happening or what it means. (I do know the difference between a mean and a median, but I can't wrap my brain around the significance of these gaps) Help me out here:

1. What is the meaningfulness of a large gap between median and mean as opposed to a small gap?
2. Large gaps tend to occur in wards with higher income. Why is this? Is it meaningful? Is it possible for it to occur in wards with lower income, and, if so, under what circumstances?
3. Why does mean tend to be higher? Is it always higher? Is it mathematically possible for it to be lower, and, if so, under what circumstances?

6 comments:

jpg said...

I think it's like this: if you have a smallish number of people in the community with obscenely high incomes, that will drag up your average but not your median. It indicates a larger income gap.

Eg: imagine a community of ten people. To keep it simple, let's put their incomes in $/hr. Here they are:

$1, $1, $2, $2, $3, $3, $4, $8, $15, $18. That's ten.

So the median $/hr is $3. But the mean is $5.70, because those few high wages are so much higher in comparison. It means

It works in reverse too (with mean higher than median) where you have, say, 80% of the population making $800k-1m annually and the other 20% making $15-40k. Your median will be in the higher strata but your average will be lower than that.

It would be uncommon for the mean to be much lower than the median because there's way less numerical distance between average middle class incomes and lower class incomes than there is between middle class and the top, say, 10% richest in Canada. $45k/yr in Canada is pretty much middle of the middle class, while middle of the poorest 20% of Canadians is about $14k/yr (http://www4.hrsdc.gc.ca/.3ndic.1t.4r@-eng.jsp?iid=22) so not that big of a gap. The richest 20% have an average income of $126k, so one person from that bracket will have more of an effect on a community's average income than one poor person. If it was possible for people to have a negative annual worth (like if you could make -$100k in a year) then that would balance out the high earners. But you don't typically have that.

impudent strumpet said...

That is such a good explanation and makes perfect sense! Thanks!!!

laura k said...

M., that is quite brilliant. Thank you!

$45k/yr in Canada is pretty much middle of the middle class,

I heard this before I moved to Canada as well as several times since I got here. I find it difficult to understand how $45K could be considered middle class. Do people own a home, a car and have some modicum of disposal income on 45K? 45K to me seems decidedly working class.

impudent strumpet said...

Might depend where you life? If a house is $100K, then middle-class on $45K is a lot more feasible

jpg said...

Hi all,

L-girl, I totally agree with you - it doesn't make much sense to take Stats Canada's framework without further comment. StatsCan tends to focus on the top 20%, bottom 20% and then the middle 60% as a single unit, when really it's hard to call the lower parts of that 60% (making maybe $35k/yr) and the upper parts of that 60% (making maybe $55k/hr) the same. It doesn't subdivide working class from middle class in the way it's usually thought of.

Maybe that has something to do with the collapsing gap between the working class and working poor. I'm always surprised at how low the averages are for that middle group - my own privilege at work.

laura k said...

Maybe that has something to do with the collapsing gap between the working class and working poor. I'm always surprised at how low the averages are for that middle group - my own privilege at work.

Here too.