I read a news article this week that said the average US family has $8377 in credit card debt.

😯

I got intrigued by the word “the **average**.” So I tried my usual fun search. I typed the phrase “what is the average” in Google and Bing search engines.

The questions that pop up in the search engines are fascinating. We should find the answers.

But I want clarification about the word “average” first. What is average? What are they showing when they say “the average something is something”?

Okay. Let us do our usual thing. Let us take a small dataset and explore the answer to your question. Given your interest in debt, let us look at data on student debt — you may relate to it more.

Great. Back to business.

I got this data from the New York Fed’s Regional Household Debt and Credit Snapshots. They include data about mortgages, student loans, credit cards, auto loans, home equity lines of credit and delinquencies. I extracted a subset of this data; average student loan balance for eleven regions in the Greater New York Area.

Let me jump in here. The first thing we do with data is to order them from smallest to largest and place the numbers as points on the line. I read in Lesson 14 that it provides a good visual perspective on the range of the data. So the data table looks like this

Excellent. Now imagine that this number line of yours is a weighing scale and numbers are balls of equal weight. For the weighing scale to be horizontal (without tilt), where do you think the balance point should be?

Somewhere in the middle? Isn’t it like the center of gravity?

Exactly. That balance point is called the average or mean of the data. You make a pass through the numbers and add them up, then divide this total by the number of data points.

Got the idea. If we use the equation on our data, we get the average debt across the 11 regions to be $33,827. The balance point will be like this.

So you see, the average student debt in the Greater New York area is $33,827. That seems pretty high.

Yeah that seems high, but let me look at the weighing scale again. There is one ball far out around $45,000. It looks like if we remove this ball, the balance point will move back. Let me try.

Hmm. Now the balance point is at $32,760. I get a sense that this average measure is somewhat sensitive to these far out points.

You are correct. The mean or centroid of the points is a good summary of the average conditions if there are no outliers. Mean is sensitive to outliers.

Looks like the Manhattan folks are influencing the average debt number.

Ah, *these New Yorkers are always up to something.*

I may want to go to college one day, but these debt numbers are scary. How on earth can I pay back such yuge debt?

Don’t worry Joe. In New York, you get your way, and Average Joe gets to pay.

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This was a nice mini lesson. I like the student/teacher dialogue that you have incorporated into the lesson. It helps to put readers into the story and breaks the material down into nice bite sized chunks.