Why is median better than mean for a typical salary?

In a previous post, I commented that PayScale's Salary Survey preferentially reports typical salaries based on the median instead of the arithmetic mean (average).

Why is the median better than the mean for measuring "typical" values? The best way to understand what is wrong with the mean is to look at how both behave in answering a simple question: how well have Stephon Marbury's Lincoln High School basketball teammates done in their careers in the last 10 years?

I started thinking again about the difference between mean and median while listening to an NPR story about Stephon Marbury. For those who don't know, he is a 29 year-old from Coney Island, New York, who plays professional basketball for the New York Knicks.

Imagine Stephon Marbury went back last year to meet with 9 teammates on the 10th anniversary of their winning a high school basketball championship. You might ask, "Where are they now? Have they done well? Did they turn what they learned playing hoops into the start of a successful career?"

I haven't actually researched where Stephon Marbury's teammates are now, so let's just make up some wages that would be typical for people in their late twenties in New York. Remember, 50% of high school seniors do not go to college, so we could expect a pretty wide range of pay: a janitor ($13/hour), a delivery truck driver ($14/hour), a retail store assistant manager ($18/hour), automobile mechanic ($20/hour), fire fighter ($24/hour),  a nurse ($25/hour), a department store buyer ($28/hour), an automobile salesman ($32/hour with commissions), and an IT project manager ($41/hour).

What is the mean (average) wage of these 9? It is easy to calculate: add up the wages and divide by 9:

13+14+18+20+24+25+28+32+41 = 215
mean wage = 215 / 9 = $23.90/hour

The median is $24/hour. The fire fighter earns the middle wage: 1/2 are lower, and 1/2 are higher. For this particular sample, the mean and median give a similar answer for what a "typical" person on that team now earns.

Now let's look at Stephon's hourly wage. Stephon played an average of 36.5 minutes over the course of 60 games last year. For this, Stephon earned about $20 million/year, or about $550,000/hour.

If we include Stephon's wage, his high school team's mean wage is $55,000/hour!

By contrast, the median wage is $24.50/hour, now half-way between the fire fighter and the nurse. The median is not significantly changed by this one "outlier", while the mean becomes a wage that no one earns: it is 2000X too high for 9 of the teammates, and 10X too low Stephon.

Like standard deviation, mean is very sensitive to the most abnormal of values, particularly very high values.  Why would one use a measure for what people "typically" earn, that is so strongly affected by atypical salaries?

The answer is historical, and the subject of a future post.

Cheers,

Dr. Al Lee

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Comments

[Adam Phillabaum]

Your example works because of the extremely varied job types (and associated wages). What about finding the "typical job salary for a database administrator in Seattle" (a much more reasonable scenario)? If there is a DBA job out there for $550,000/hour, I would love to know about it. But I doubt it exists, and therefore the outliers are much closer to your typical salary.

In general, I have a feeling that in these more typical scenarios, the mean, median, and perhaps even the mode will all be very close together.

[Leslie]

May I please have a job description for a General Doctor and also the Salary. Sorry I need this information and I will be very thankful if you can e-mail it to me by today 12/13/07. Thank You Leslie E.

[Javier Garza]

What is the average total compensation package for a internal audit position in kuwait?

[Floyd]

I use mean and median to find the average lottery numbers are drawn. If the median is more accurate I really need to know.

Thanks for the post so far.

[Kristi]

This helped a lot because I'm doing my senior project on Physical Therapists and now I better understand their salary. This is neat way to calculate it.

[F Bruce H]

Average and median values are relevant when comparing wages among peers or among workers whose wages fall within a specified band, but might not be very useful when seeking a job for which there are few openings and/or for which unique skills and/or experience are required. How should we evaluate wages (mean, median, or what?) for these latter, less-common positions?

[Malcolm]

Here's an example where the average is more meaningful. The wages of 3 friends, 2 of whom do quite well, are as follows: $550,000, $15 and $500,000.

The mean is $15, not too meaningful.
The average is $525,008, more realistic I think.

[Mr. Marx :)]

It is a matter of honesty that we include atypical salaries in our measure of what people "typically" earn. Thus, it is a dishonest to focus on the median rather than the mean.

It is not a matter of what the typical poor guy earns that establishes the value of money, and thus the meaning of relative earnings. Atypical earnings affect the value of everyone's money because the relationship between individual assets and overall collective assets determine buying power. If an "outlier' is getting paid so much that everyone else's individual income looks puny next to the mean then that is a fact worth considering. Moreover, it is - as a matter of fact - a situation in which a lot of people are getting paid a sum that is worth very little. To suggest otherwise serves no meaningful purpose but to hide this fact.

[Matt]

Which measure of central tendency is most useful, median or mean, really depends on what the measurement will be used for. If one is doing economic calculations, and needs to know the amount of money consumed by a particular group, then mean may be more helpful. For an individual predicting his or her future salary if he/she goes into a particular field, the median figure is more relevant.

While the writer makes this point using an extreme example (the outlier professional athlete versus normal jobs), this trend is still seen even within most job titles. Often the top 5-10% in a field earn vastly more than others because of preexisting work experience, industry knowledge, connections, or more effective work habits. The top 5-10% of law school graduates from most respectable law schools start at $120-$160k while most law school graduates start around $45-$70k. (For top 10 law schools, the percentage earning $120-160k is a bit higher, but the point remains the same.) The median is more representative than the mean of what most people earn, even within a profession.

Similarly, in some fields there will be outliers on the low side; some may not have qualifications that others in the field typically do. For example, most MBA graduates have substantial professional work experience prior to enrolling in MBA programs. Some students do not, and perhaps they may take lower paying positions upon graduation.

[teachersalary]

Average pay. Median pay. Base pay. Its all garbage! It's all dangerously misleading if not intrepreted carefully. What is important and often underappreciated are your benefits and value of future pay raises in your contract. For years our school board relied on these stats to make important compensation negotiation decisions. teachersalarydata.com has provided us with meaningful data comparsions to other districts.

[josh]

I just have to say that average pay would not be fair to the people that make more money. The average for me would be 12 dollars where as i would actually in factly make 41 dollars. Utterly ridiculous! It's a shame i say! I do not want that for myself

[darlene]

I have to infact agree with what josh is saying. He makes some good points in his argument. For my rebuttle, I am the janitor at WHS and i find it utterly disgusting that i work just as hard as the next guy! life throws you stuggles, you gotta learn to throw them back, if ya know what im saying. ;) XD

[josh]

I hear ya! Working hard to get ahead is always a struggle but you just gotta keep on going. I see your point as to if you work just as hard as me or even less equal pay might be a good idea. IF it is all averaged out then maybe there won't be a recession! And we can all hopefully get this economy kickstarted back up!
Peace.Love.

[darlene]

great choice of words josh! you really put it in perspective for me. im a single mother of 7 working hard for a little and i know just as much as anyone one else if not more what it means to work hard. being a janitor can be tough but when i see the smile on the kids faces when they walk into a lunch room of clean tables, it makes my whole day worth while. LIFES GREAT. keep lovin it. :P

[josh]

thats a good motto darlene! are you working hard or hardly workin'? heh just kidding i know as a single mother of seven you must work hard! good luck to you and your family. btw do you have a email address? we should talk over dinner =)

[darlene]

yes, in fact i do. its darlene21@aim.com! would your wife be joining us ;) ?

[josh]

oh well you see.. im single as well. its nice to find someone who enjoys accounting as much as i do tho! we have some good opinions we need to get them together and talk about them on a date. sayy- saturday? do you live in the new hampshire area? il give you a ring! until then<3

[darlene]

i do not live in new hampshire, but i do live in maine! ive always found long distance relationships so romantic! ill gladly take the trip to new hampshire, what part? is chili's okay? its my fav. gotta have my chicken crispas if yah know what im saying. i just love em!!!