Average/Median–Or Lying With Statistics

I have previously mentioned–and sometimes quoted–my friend Morton Marcus. Marcus   is an economist; he is retired from Indiana University, where for many years he headed up the Kelly School’s business research center. Morton and I have been friends for a long time, and have just co-authored a book on the women’s movement. (More on that when it’s published.)

Morton also writes a weekly column on economic data  called “Eye on the Pie,” explaining in relatively simple language what various data points tell us about Indiana. That column runs in a number of the remaining small newspapers around the state. In a recent column, he made a point that I think is so important I feel compelled to share it.

Morton fashioned his column as “A note to Gov. Holcomb,” and began by saying that normally, he doesn’t write to the Governor.

But this week is different. A few days ago, you gave your “State of the State” address to the General Assembly. It was a nice talk and very well presented.
You had some good ideas for our state, but, and this is awkward for me to say, you don’t have a staff that keeps you from making the same mistake time-after-time. You’re not the only Governor who makes this mistake. I’ve known them all from Gov. Whitcomb onwards and they all make the same mistake.

And what was that mistake? (I must admit, it’s an error I have often made too.) Let Morton explain:

Almost always the Indiana Economic Development Corporation (IEDC – bless their hearts) tells us the average wage going to be paid by a firm they have arranged (lured, bribed) to open or expand in Indiana.

Most of the media (bless their hearts) regurgitate the press release because they don’t have the time or energy to remember that the average is the mean of a set of numbers. It can be heavily influenced by extreme (high or low) values.

The median, however, tells a different, more meaningful story (if you’ll excuse a little pun there). The median is the wage above which half of the employees will get paid and below which the other half of the workers will be paid.

Let’s say the top gun gets paid $150,000 per year. The #2 gets $75,000, the other eight get $30,000 each. That’s a total payroll of $465,000 for ten employees or an average (mean) annual wage of $46,500. Yet the median pay is $30,000. That’s $16,500 (35%) below the IEDC-advertised average.

From what I hear, Governor, you’re not the type who intentionally misleads or lies to the people of Indiana. But by using the average (mean), rather than the median figure, you’ve been passing on some real whoppers over the years.

If I might have just a bit more of your attention, let me note the average (mean) annual pay for all occupations in Indiana in 2021 was $50,440 (37th in the nation) or $12,110 (32%) above the median Hoosier pay of $38,330 (39th among the 50 states).

With just two years left in your term of office, you said you were going to work harder than ever for all Hoosiers. Maybe you could get IEDC and your staff to give you the most accurate, realistic numbers. Then the people of Indiana would not continue to be misled by excess enthusiasm and just plain ignorance.

When I read this column, it immediately reminded me of a book I read several years ago, debunking several of the claims that were then being made about the “failures” of the nation’s public schools. The authors noted that much of the data being uncritically reported about “averages” was similar to the rather misleading result one would get when averaging a mouse with an elephant.

If you average my income with that of Bill Gates, you’ll come up with a pretty impressive average…

Actually, Morton’s column does inadvertently highlight a failing of the education system: too many Americans (including, I am sorry to say, the one writing this blog) are innumerate–lacking a basic knowledge of mathematics and arithmetic. That innumeracy encourages the use of statistics to mislead. As the saying goes: statistics don’t lie, but liars (and innumerate folks) do use–or misuse– statistics.

The Governor’s error perpetuates the erroneous belief that Indiana is succeeding with an economic development approach that relies almost entirely on keeping the state’s  taxes low–and ignores the fact that those low tax rates prevent the state from spending tax dollars to achieve a quality of life that would be far more likely to attract the businesses and skilled workers we need.

More on that to come….


  1. In 1979 the Indiana Statesman, the ISU newspaper, had a front page headline ” Average Salary for 1979 ISU Graduates $1.5 million” of course the student run newspaper understood the average was skewed by Laryy Bird’s $3.35 M contract with the Celtics and the low pay of teachers in 79 that was around $6,000/year. It was funny at the time, but teachers are still making the equivalent of the $6,000 salary. So when tje current GOP claim the average salaries of teachers is blah blah blah, they know they are lying.

  2. Supposedly Mark Twain said there are three types of lies: lies, damned lies, and statistics. Now, just about everything clever ever said is attributed to him and I have no idea if he really did, but either way it’s a fine, accurate statement.

    Whenever anyone talks about averages it’s ALWAYS good policy to ask yourself is they are using mean or median. On the bright side, no one uses mode – so at least there are only two options to check.

  3. As a graduate with an economics degree I want to thank you for writing about this today.

    It continues to amaze me that so many people don’t notice the misleading ‘stats’ used by economic development folks. Of course they need to make the numbers sound a whole lot better than they actually are because how else could they justify their own titles and typically bloated salaries?

    However, they don’t fully succeed at always fooling the general public. When those long awaited businesses finally advertise available jobs at much lower wages than public officials spoke about in the distant past, they often find the much of the public uninterested in working for the ‘true’ wage level for those jobs. The corporations/businesses and government officials can then publicly whine about nobody wanting to work. Never mind that they knew all along that they had misled the public many months or years ago. This scenario seems to work out well for the economic development and government officials who were originally applauded for bringing new jobs to the area. Eventually, that bed of roses becomes thorny when the people with marketable skills or college degrees choose to leave Indiana for greener pastures and much better pay.

  4. It’s good to see that Dr. Marcus is still fighting the good fight. I pray that one day, his message will hit home. BTW, I doubt the governor’s staff were unaware of the difference. They chose the number that looks better for more practical and political reasons.

  5. Politicians (who, let’s face it, are salespeople of themselves) employ many of the tools of the sales trade. One of those is, never to communicate the whole truth, which is often ambiguous when it comes to whatever you are trying to convince potential customers to buy, but find some truth that is most convincing, if less comprehensively informative.

    “Median”, as compared to “average”, are indistinguishable to most people so whatever more accurate meaning you are trying to get across by choosing between the two terms will be lost to them. Plus. the Governor is not really trying to convince voters accurately of the state of the State but to make them feel good about their government.

  6. thanks for bringing up the wage issue.the office of some sort of governance would this issue to make certain it was confusing. in my world of being publically educated,and blue collar,ive often heard that wage mean mentioned,many a time. though its not said as mean,it damn sure is. when a company relies on a goverment office to further their ambistions elsewhere, its usually wage focused and then getting materals/housing and transport and now IT. switch to the other subject of what tax breaks and loop holes they get to enjoy at the states expense over needs. happy medium,not. does the state and fed offer a tax plan to add some needed profits sharing or bounuses? nope, the reality is the shareholders get the goodies while the workers get to live thru whatever the shareholders,corps and gov officials reap, while we get to sweat out if that job is a benifit to man and longivity. sure we could invest,but heck,they dont have that plan in most buisnesses,and like myself,i find profits given to shareholders stealing the wages out of those who did the work . todays greed (buisness sense)is to make them live next to poverty, with little sight of the light at the end of a train tunnel.heck of a economic system the goverment agreed to devise into economic slavery for the working class. keep the worker guessing,keep worker confused,keep em locked next to poverty,and they will provide out of fear.(should be on every state flag)

  7. Maybe a better way to inform the public would be a graph showing the projected salary range broken down into 10 thousand dollar increments and the number of employees projected to be hired in each category. Of course, that would only be seen by the reporters informing the public if they ask for it. That information must be available in order to calculate the mean and median. Once again we run up against a dearth of quality local journalism.

  8. I took a degree in economics before going to law school, became a Keynesian, and (using a slide rule in those long ago days) took a required course called “The Statistical Evaluation of Economic Data,” which we students (perhaps mercifully) shortened to “Stix.” It was there I learned of the evils some employed in the world of averages, means and medians, evils still notably in vogue in the political and corporate and other worlds of accounting alchemy available for manipulation by governors, CFOs et al.

    Consumers of such glowing accounts of political and corporate wizardy are uninformed of truth in such worlds due in part to emptied newsrooms and consumer disinterest in such technical matters and rely on what politicians and accountants tell them without questioning their respective slants on the data presented.

    Averages are especially poor measures. As I tell people who are interested enough to listen, I am filthy rich when my income is averaged with that of Warren Buffett (or perhaps lately with that of George Santos, who employs measures we were not taught in Stix).

  9. My favorite stats book is titled “How to Lie With Statistics”. Bottom line the average person does not have a clue when it comes to stats, including those with college degrees. It is not a course that attracts many nor do they have the background to understand the basics such as the ways to describe the middle of the stats, mean, medium & mode. However, the snake oil salesmen such as tRump and others like him certainly know how to deploy stats in such a way to support their agenda(s).

    It should be noted stats is the course that trips up students from the “soft sciences” such as education, sociology, etc causing them to drop out of graduate school. I was able to be successful in stats as I am not the average educator when it comes to mathematics as I have an engineering background and worked as a machinist & tool maker for several years. Math was the major “tool” I used in my trade including trig and plain & solid geometry. Stats was one of the courses required for my AS degree in Quality Control.

  10. Stan: thanks for sharing your math brilliance with us. BTW: it’s “median”, not “medium” — we biologists take stats, too.

  11. Good, Max. And when the brilliance gets to be too much, we can simply remind the brilliant one that it is PLANE geometry…not plain. This stuff is in his field. He should know. Sigh!

  12. There is a more current book called “The Flaw of Averages” by Sam Savage (2009). For an oldie, but a goodie, see M.J. Moroney,
    “Facts from Figures” (1951) which I bought for $1.25, “back in the day.”

  13. I know you are busy, Jack Smith, but, I miss your wisdom when you are away. Thank you very, very much.

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