[sebastiennight]

I'm not sure I catch your explanation, so let's try with some simple numbers and you'll tell me where I'm wrong.

I have a family of 10 people. These people have, respectively,

$0 ; $0 ; $1 ; $5 ; $49 ; $51 ; $190 ; $8,000 ; $150,000 and $1,000,000.

What's the median amount of savings in this group?

And what amount would complete the sentence : "50% of people have ..."?

[throw-qqqqq]

The median of those ten numbers is 50.

If the count of observations is even, it is usually the arithmetic mean of the two mid-points, so (49+51)/2 in this case.

The median does not have to be in the finite set of values.

Maybe Wikipedia can explain better than I can: https://en.wikipedia.org/wiki/Median

[sebastiennight]

You didn't answer my second question. Yes the median in my example is $50. Thus it would be accurate to say "50% of people in that sample have $50 (or $51)". But not anything further than that middle point.

Back to the original post:

I'm assuming that "three months of expenses" would be roughly $6,000.

The parent post had the median at $500.

1. Given the sheer number of adult Americans (hundreds of millions of observed data points), wouldn't you say it's quite likely that the two mid-points are very close to each other (eg $499.97 and $500.02)? But definitely not (-$5,500) in debt for one mid-point individual vs $6,000 in savings for the next individual (which comes out to $500 in median and "top half has $6k")?

2. In the first scenario (almost continuous curve at the midway point), how likely do you think it is that somewhere right after that $500 mid-point, there is a huge discontinuous jump to $6,000 to accomodate the idea that the rough top half of observed savers has "3 months of expenses" saved?

3. Is there any other scenario I'm not foreseeing, that can reconcile: "the median is $500" with "the top 50% have $6,000+ in savings"?

[throw-qqqqq]

> You didn't answer my second question

I purposely didn’t because strictly that is not a median. Stupid example: median of 1,2,3 is 2 and 67% >= 2 here. We do agree that as N grows, the difference shrinks (to the point of no meaningful difference).

My point was that mathematically there is no contradiction. Let’s say half the population has $200 monthly expenses (3mo is then $600 saved), the median is $600 and it checks out.

That is a stupid assumption though - because who has such low expenses.

> I'm assuming that "three months of expenses" would be roughly $6,000

You then assume that we must be talking about the upper half, but that isn’t given.

We have to make SOME assumptions though, since the statement is underspecified: the OP didn’t specify what 3 months expenses means. It is unlikely that 50% of the US population have the EXACT same expenses, so I assumed an “on average” was missing somewhere which further relaxes the constraints.

I objected to your statement that the math doesn’t check out. There are many ways it could check out.

We came at this with different assumptions. I don’t think we fundamentally disagree and I didn’t mean to bicker.

[sebastiennight]

Thanks for your response.

I appreciate you taking the time to geek out on some statistics with me (and you even had me look up medians again because I was confused at your reply!)