# The Difference Between Median Student Debt and What the Median Student Owes

There’s a great article in The Atlantic on student debt, and it’s well worth a read. But it makes what I believe is a common mistake on student loan debt. Check out this paragraph…

When teenagers are forced to take out loans in order to pay for their education — the median graduate leaves school \$12,800 in debt — it acts as a tax on their future wages. It postpones their ability to settle down, buy a home, and have children. That’s tragic for them, and it’s tragic for us, because it means less money will flow into other, more productive parts of the economy.

That figure comes from the Fed’s Liberty Street Economics:

The average outstanding student loan balance per borrower is \$23,300. Again, there is substantial heterogeneity in balances of individual borrowers. The median balance of \$12,800 is roughly half the average level…..

Notice, however, the difference.  This is the median balance — this is the median value of loans, not what the median student owes. That’s an important distinction, since only about 66% of students take out loans.

To consider how that might affect things, consider this set of numbers, where the median is 5.5:

{1,2,3,4,5,6,7,8,9,10}

Now what happens if we add our 33% of zero values to this? Well, if this set represents 2/3 of the values, then there are five zeroes to add in to fill it out:

{0,0,0,0,0,1,2,3,4,5,6,7,8,9,10}

Our median now drops from 5.5 to three. Now admittedly, our example is not a normal distribution, but we’d still expect a drop from the 50th percentile to the 33rd or so, which should be substantial.

This seems trivial — I agree that student loan debt is an issue, and the the number of students graduating with debt is a problem. But if we are to address the problem effectively, knowing the precise scale and shape of the debt is important.