Tag Archives: median

“The average Australian is a suburban Frankenstein”?

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One columnist is not pleased with the idea of the average Australian in the suburbs:

Earlier this month the Bureau of Statistics, apparently hoping to deter Wayne Swan from cutting its allocation in the May budget, made a grab for publicity with a report on the characteristics of “the average Australian”. In the process it broke its own rules.

The ABS applied mathematical magic to data from the 2011 census and sent the media off in search of a blonde brown-eyed 37 year old woman with two photogenic children aged nine and six, two cars and a mortgage of $1800 a month on her three bedroom home. Edna Everage’s granddaughter was born here (like her parents), describes herself as Christian, weighs 71.1 kg, and works as a sales assistant…

Start packing your bags. The ABS decision to build a suburban Frankenstein for the sake of a publicity boost risks returning us to the point in recent history when certain people were labelled “unAustralian” if their language or behavior did not match the world view of Alan Jones, John Laws, Neil Mitchell or Andrew Bolt.

The ABS has played into the hands of those titans of talkback who like to keep the message simple. They’re not interested in this qualifier the ABS included at the end of the report to salve its conscience: “While many people will share a number of characteristics in common with this ‘average’ Australian, out of nearly 22 million people counted in Australia on Census night, no single person met all these criteria. While the description of the average Australian may sound quite typical, the fact that no-one meets all these criteria shows that the notion of the ‘average’ masks considerable (and growing) diversity in Australia.”

The columnist may indeed be correct that the best way to do this would have been to use medians, rather than averages. But, the bigger issue here seems to be the idea that there is a “suburban mold” that Australians need to fit into. Not everyone likes this image as the suburbs are often associated with homogeneous populations, consumption and behaviors to keep up with the Joneses, and middle-class conservatism. Regardless of what the statistics say or whether a majority of Australians (or Americans) live in the suburbs, these suburban critiques will likely continue.

The median college loan debt: $12,800

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Growing calls for ways to deal with college loan debt can lead to a statistical question: just how much does “the average” college student owe? Here are some of the figures:

Meet Kelli Space. She went to Northeastern University to get a degree in sociology. And she graduated in $200,000 of student loan debt. In the economy’s newest trillion-dollar crisis, she is the 1 percent.

Kelli is not the face of America’s student debt problem. Among the 37 million people in this country with student loans to pay off, the median balance is $12,800. A whole 72 percent of borrowers have less than $25,000 left in debt, according to data from the Federal Reserve Bank of New York.

No, students like Kelli are the rarities, the white rhinos. Only about 5 percent of borrowers owe more than $75,000.

The key figures for me: the median is $12,800, meaning that half of people with student loans have less than this figure, half have more. Yet, nearly three-quarters of those with loans have less than $25,000 to pay off. Only 11% have more than $50k in debt.

So why do we keep hearing stories about those who owe mega amounts of money? Perhaps we might think of them as canaries in the mine shaft, students who show how bad the college finance system might be today. But, on the other hand, the statistics suggest that these students are rarities, people who have unusual debt. From these anecdotal and relatively rare stories, it seems like there is a pattern: a student goes to a prestigious school banking on the name of the school to pay off. (One common argument you will find online is that the major should be blamed – this usually puts more creative disciplines, the humanities, and subjects like sociology at the center of blame.) But, the name doesn’t always pay off, the student can’t find a good enough job to start paying off these debts, and the interest just continues to grow.

Overall, we need to work with the statistics more than the anecdotes: most college students do not have more than $25,000 of debt. This is not a small amount but it can be tackled (though the economy doesn’t help).

More $1 million lottery winners each year than NBA players since 1990 that have career earnings over $1 million

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I’ve written before about using the average vs. the median salary in the NBA lockout discussions and here is some more fuel to add to the fire: there are more $1 million lottery winners each year than NBA players who since 1990 have had career earnings of more than $1 million.

I want to call foul on the mainstream media. As I mentioned, a majority of the players in the league make less than $2 million, and yet people like Stephen A. Smith throw around that $5 million figure as gospel. We keep hearing the NBA lockout being described as “millionaires versus billionaires”. But most NBA players won’t become big earners like Kobe and LeBron. Here’s a fun breakdown:

Since the 1990-1991 season 1461 players have entered the NBA and of those:

  • 490 — or 33% — never earned $1 million in career earnings*
  • and that means… 971 have earned at least $1 million in career earnings*
  • 752 have averaged a salary of at least $1 million per year*
  • 643 have earned at least $5 million in career earnings*
  • 165 averaged a salary of at least $5 million per year*

As we can see, less than half of all NBA players in the last 20 years — the period of time where NBA salaries have been at their highest — have hit that $5 million mark over their entire careers. Just over one third — 33% — of all NBA players in the last 20 years have not even hit the $1 million mark in career earnings. And these numbers have been adjusted for inflation!

Here’s a fun comparison: on average, 1600 people win a lottery of at least $1 million every year! That’s right; the lottery has produced almost twice as many millionaires in the last year as the NBA has in the last twenty years!  The popular perception is that once a player enters the NBA they will earn millions and millions of dollars. The truth is that many players don’t hit that high mark.

Both events, winning the big lottery jackpot and becoming a NBA player, are statistically unlikely. However, I suspect that most Americans would say that winning the lottery is much more unlikely. But this blog post points out that even when players do make it to the NBA, a third don’t rake in the big career earnings associated with professional athletes (measured here as $1 million).

This would make for an interesting discussion starter for any professional athlete’s union: should the union be more concerned with allowing a smaller percentage of the athletes maximize their salaries or be more interested in guaranteeing a baseline for the majority of the league that are not stars?

The lottery figures themselves are interesting:

According to the TLC television show, “The Lottery Changed My Life,” more than 1600 new lottery millionaires are created each year. That doesn’t include people that have won jackpots of, say, $100,000 because than the number would be much higher. Still, 1600 is quite a high number.

If 1600 win at least a million in the lotto every year, it means that there are more than 130 each month, more than 30 each week, and more than 4 each day. That’s a lot of winners.

It would be interesting to see more documentation on this.

The problem with using averages as illustrated by the average salaries of NBA players

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In negotiations between NBA owners and players, the topic of the “average player salary” has come up. This discussion illustrates some of the issues involved with  using averages and medians:

Here is the “average player salary” for each of the major U.S. professional team sports, based on a variety of sources using the most recent data available:

NBA: $5.15 million (2010-11)

MLB: $3.34 million (2010)

NHL: $2.4 million (2010-11)

NFL: $1.9 million (2010)

From the public’s view, these numbers are high in all four sports. But players and agents argue that these averages obscure important distinctions including the value of certain positions over others (the quarterback in the NFL versus the punter) and the size of the roster (fewer NBA players, more NFL players).

One common solution to problems with averages is to instead use a median. Here is how this might change the discussion in the NBA:

“It’s the median salary that’s more important,” NBA agent Bill Duffy said. “Look at the Miami Heat as an analogy here: You’ve got three guys making $17 million and probably six guys making $1.2 [million]. So that’s a little misguided, that average salary.”…

It is not unlike, Duffy said, news stories that cite the “average” U.S. household income as opposed to the median. The latter figure, according to the most recent U.S. census, was $50,233. If you were to average in the dollar amounts pulled down by Wall Street bankers, Ivy League lawyers, certain public-union employees and yes, professional athletes, that number would jump considerably.

Curiously, neither the NBA nor the NBPA seems to make much use of a median player salary.

“We use [average] because it’s the most commonly used measure and best reflects the amount of compensation that the NBA provides to players across the league,” an NBA spokesman said this week. “In addition, it’s the measure that both we and the union agreed upon in the CBA.”

In the NFL, the median salary is approximately $770,000 — about 40 percent of the average.

In the NBA, using USA Today salary figures for the 2009-10 season, the estimated median salary was about $2.33 million. That’s still about 46 times what the median U.S. household earns, but it is less than half what the max-salary-bloated “average” is.

What happens in these sports is this: a small number of star athletes make huge amounts of money, pulling the average for all athletes up. If you use the median instead, where 50% of the players make more and 50% more make less, it suggests that more of the athletes in each sport make less. Particularly in the NFL which has bigger rosters, the difference between the average and the median shows that many players make very little.

It is interesting that the NBA spokesman said the two sides had agreed in their Collective Bargaining Agreement that they would use the average salary figure. Was this really a point of contention negotiations or did no one really think about the consequences? What was the thinking behind this for the players? If the union was focused on helping all of their members, perhaps they would focus on the median, suggesting that they are strongest when all of their members are well taken care of. This lower figure might also look more palatable to the public though it is unclear whether public perceptions have any influence on such negotiations. However, if the union was more interested in making sure that individual athletes could receive the biggest possible payouts because of their athletic exploits, then perhaps the average is better.

Two takeaway points:

1. Averages and medians are both measures of central tendency but they are open to different interpretations. People need to be clear about which they are using and which interpretation their number interprets.

2. It will be interesting to see if the new CBA is based on average or median salaries.