Personal Finance 101: How Averages Lie

personal finance 101Whenever a personal finance writer – or a writer of any kind – wants to make a bold, shocking point, they’ll often pull out an “average” of some set of numbers. That average, when read without further investigation, is often really shocking. Could that really be true? Here are some examples.

The average square footage of single-family homes under construction fell dramatically, from 2,629 in the second quarter to 2,343 in the fourth quarter. (from USA Today)

The average credit card debt per household — regardless of whether they have a credit card or not — was $8,329 at the end of 2008. (CreditCards.com statistics)

The average 401(k) fell 27% in 2008. (MSN MoneyCentral)

Those numbers seem fantastic. I grew up in a home that had about 800 square feet and currently live in a home that feels huge to me at times and is just shy of 2,000 square feet. The average home has over $8,000 in credit card debt? That’s well over $100 a month just in interest!

However, if you start teasing those numbers apart a little, a few interesting truths reveal themselves.

Let’s look at the first one. The average new home has 2,343 square feet in floor space. Well, let’s assume that one in five homes is a 7,000 square foot McMansion. That means that four out of five newly built homes are just 1,200 square feet. In other words, if you lined up all of the houses that were built in the last year side by side ranked by their size and chose the one in the middle, it would be far less than 2,400 square feet.

How about the average credit card debt? Again, the huge ones skew the average. If you have three homes with no credit card debt, one with $10,000 in credit card debt, and one with $30,000 in credit card debt, the average credit card debt of those homes is $8,000 even though three out of five of the homes have no debt at all. The facts back this up – the majority of American homes carry no credit card debt.

That third one is also interesting. The average 401(k) fell 27% in 2008, yet the stock market (as judged by the S&P 500) dropped 37%. What does that mean? Lots of investors out there didn’t have all of their eggs in the stock market basket.

Whenever you hear a news report or read an article where someone quotes an average, you should get your guard up because there’s a solid chance that a skewed story is being presented.

How is it skewed? Quite often, when we hear “average,” we compare our situation to that number. Yet, as we’ve seen above, the vast majority of people are often well under (or in some cases over) that average. That average is misleading, and if we compare our own situation to that average and use it as guidance for moving forward, we can often mislead ourselves.

How can you figure out the real story? One big first step is to look at the exceptional people on either end. Take the house square footage example. The biggest houses built would be over 10,000 feet, while the smallest ones would be around 1,000 square feet. Then, look at the average. The end that the average is closest to is where most of the people actually are. After all, if there are 9 people building 1,000 square foot homes and 1 person building an 11,000 square foot home, the average is a 2,000 square foot home – but none of them are actually building a 2,000 square foot home.

Good luck.

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  1. Broke M.B.A. says:

    I guess these “averages” lose their shock value when compared to the “median” that you are referring to. I don’t think it is necessarily bad that people present stats in this manner, but it is a good idea to dig a little deeper when hearing such statistics.

  2. Johanna says:

    They actually collect data on the median new home size as well as the mean (or “average”). In early 2008, the median size was 2291 square feet, and in the third quarter of 2008 that dropped to 2090 square feet. So it’s a bit less than the mean, but not too much.

  3. Mike Piper says:

    “Averages lie” seems to be one of the lessons that all investors learn early in life. “The stock market averages an 8-10% annual return.”

    True! But if only it were as easy as that makes it sound….

  4. Daniel says:

    Statistics are just data, it’s what you do with them that counts. They are meaningless unless you dig a little deeper and find out what it all adds up to.

  5. Finance Nerd says:

    Here is an interesting example of the “flaw of averages.”

    It’s possible that some people have 3 arms, but they are more than canceled out by the people with one arm (or none). So, the average number of arms per person is something like 1.99+

    This means that MOST people have an above average number of arms.

  6. AnnJo says:

    If you put 10 birds and 10 dogs in a room together, each animal on average has three legs, one wing and half a beak (at least until the dogs eat the birds)!

    The frequeent use of the “average” in so many news articles is evidence of how ill-informed most Americans, and especially journalists, are about statistics. It has its uses, but the median would be a much more useful figure for these kinds of articles.

    By the way, that “credit card debt per household” figure includes balances on business credit cards, so it’s even more misleading than appears on its face.

    One would expect the losses in 401(k)s to be lower than for the S&P, because the S&P measures only the stock market, and 401(k)s invest in bonds and cash instruments as well as stocks.

  7. Little House says:

    Maybe using the median would be a better way to gauge what the majority of the population is doing. Especially if the majority of the population lives in a smaller house, yet the larger square footage homes are throwing off the “average”. It wouldn’t throw off the median, or middle number.

    And as for consumer debt, it’s too bad that there aren’t more articles stating that most people don’t have credit card debt. That fact threw me off and makes me want to pay down the rest of my line of credit!

  8. Peggy says:

    In fourth grade, I learned that there are three ways of computing an average: mean, median and mode. All three are called “averages.” You can take a piece of data and skew it any direction you wish to suit your purpose. For more information, see “How to Lie with Statistics” by Darrell Huff.

  9. d_2 says:

    i think the real problem is that in a population that is normally distributed, the mean value actually does describe something sort of right in the middle, something of “average” value. (take height, weight to some degree, etc)

    since we typically only learn about normally distributed things in school, and many phenomena in the real world begin to approximate the normal distribution the more they are observed, our intuition that “average” is a descriptive statistic all by itself is confirmed.

    what we really need are several measures of the distribution: several percentiles (5,25,50,75,95 for starters) and the min/max values, the mode, the average, etc. if every article that described an average also included that information, we’d be in much better shape to judge how well the average described the distribution.

  10. K says:

    It’s easy to point at means and averages and make them a straw man for there being “no good statistics”. I’d prefer the argument that “reporters who can tell a good story with statistics are hard to find.”

    Means/averages are used in statistical analysis because they are additive — you can, within a set of statistics like income and debt, sum various averages together toward a whole and develop a more comprehensive picture. Medians are not additive. Medians are often similar to the mean, and if you have them both together (as Johanna mentioned), you can use them to gauge how big of a difference you are likely to see in the outlier values. If your mean is significantly higher than your median, it would indicate that there are outliers on the high end that are having a strong influence on the mean’s result. So in the housing example, if we have a mean/average of 2343, and the median is 2090, the relatively small difference is actually demonstrative of the fact that in housing square footage, most of the values in the set are clustered within a relatively small min/max range. And your last paragraph makes me want to get started on additional stats theory that would probably make people’s eyes glaze over, so I’ll stop here. :)

    As you rightly point out, financial reporters who use “average” as a substitute for “typical” are doing a disservice. Nevertheless, saying that if you read “average” in a news story you should get your guard up is no more helpful.

    One last note – due to the stringent nature of statistical analysis as it applies to consumer research, there is often a time lag associated with its presentation. The MSN article you cite, for example, is referencing data that was presented in 2008 and collected for the most part in 2007. Again – this is something that financial reporters should be more careful about, but generally aren’t. It’s never a bad practice to take a few minutes and go back to the source data and come to your own conclusions.

  11. Greg says:

    The average number of blogs read each day is 2.4.

  12. Craig says:

    It should be more averages based off of people similar to you. When you look at averages on a large scale it will always be skewed.

  13. Kate says:

    To Peggy:

    Not quite — mean, mode, and median are each measures of central tendency, but NOT all are the ‘average’.

  14. I like the point you are trying to make here, and I do agree that statistics can be very misleading. However, I think it is important to note that the outliers you mentioned as having messed up the averages would not bear such significant weight in studies of much greater magnitude. Sure, when the sample size is only 10, one outlier can really screw up the data, but in sample sizes of thousands or hundreds of thousands, even a dozen of those outliers will have little impact. I do understand that your examples were small for the simplicity of explanation, but my point is that I don’t think the outliers are the real problem in why statistics lie…

    The problem is that statistics (even from valid, professionally performed studies) can be manipulated to prove just about any point. I’m not saying they are lying, just that statistics can be manipulated by changing the perspective (i.e. analyzing a smaller portion of the overall data).

    I’ll leave you with a quote from comedian Steven Wright “42.7% of all statistics are made up on the spot.”

  15. Oskar says:

    The Avarage person has 1,95 legs, 1,8 children, 0,4 dogs and 0,3 cats etc etc however I don’t know one person like that:-)

    Back to houses, I don’t think that a family earning an ‘avarage’ income can afford an ‘avarege’ size house how does that add up?

  16. Dan says:

    oh boy the ignorance with statistics!
    the “problem” with averages isn’t the average, it’s those that misuse them.

    An average simply explains a set of data within a certain amount of confidence. That confidence level, nor the error in data gathering are rarely, if ever discussed, thus leaving an “average” reader to their own machinations.

    We get closer when articles mention a statistic and offer further information such as; +/- and how many were surveyed.

    Bottom line: Averages NEVER Lie!!!!!!!! EVER!!!!! You CAN’T SKEW math!!!!!! People CAN misrepresent, but math is constant. So please don’t act all high and mighty smarter than mathematics. Go out there and actually LEARN how math works, then you won’t be caught with misinformation.

    (And judging by most of the comments out there, I guarantee that the average poster has never taken a collegiate level statistics class, or if they had, did not do so well)

  17. K says:

    @Dan… would that be the “average” poster, or the typical poster? :)

  18. kristine says:

    I like my averages broken down into pie charts, with ranges that represent the larger plateus. It’s good for us visual learners.

    And yes, averages can be misleading, but you need to start somewhere. If a faucet drips erratically, you would still let it fill up the bucket to see how long it takes to drip a gallon. And you might try again the next day to see if it is dripping faster. The average just shows trend, not breakdown. It’s the change up or down that makes it a useful stat.

  19. Kevin says:

    @Oskar (#15):

    “Back to houses, I don’t think that a family earning an ‘average’ income can afford an ‘averege’ size house how does that add up?”

    Oskar, my friend, I think you’ve just uncovered the root cause of the entire economic collapse that occurred last year. If only you’d been asking this question in 2001 or so, this whole mess could’ve been avoided. :)

  20. That is one of the principles of averaging I think, to discard the extreme highs and lows?

    John DeFlumeri Jr

  21. Statistics are analyzed differently depending on who uses them. Two people can use the same data set to “prove” their point. A person has to dig deeper, whether in money or politics or anything else in life.

    Dig deeper!

  22. Mary W says:

    The book I read in college that has helped me most in life is “How to Lie With Statistics” by Darrell Huff. Original copyright is 1954. It was used in my statistics class in the 1970s, and I believe it is still in print.

    It runs through the things Trent discussed and more regarding, well, how to lie with statistics. Short, well written, easy to understand book.

  23. Jim says:

    The median size house in the US is about 1700 sq ft. The mean size of new houses is bigger because its skewed high by large mcmansions and skewed high because new houses are generally larger than old houses but most people don’t live in newer houses and few really live in mcmansions.

    Its important to look at the kind of statistic they’re citing (median or mean) and also to consider what the population they’re talking about. In the case with ‘average new houses’ its easy for people to apply that stat to think that most Americans have houses this size which is not true.

  24. Lenore says:

    I really liked this article, Trent, because there’s so much misinformation and “spun” news to wade through on any given day. Thanks for the reality check! I could also use a refresher on sneaky advertising tricks and other abuses of logic as we move into the hype-filled holiday season.

    Does anyone know if Black Friday is REALLY the first day of the year that retailers turn a profit? I can’t believe hardware, furniture or many specialty stores are that dependent on holiday shoppers. Is this cliche statistic based on Hickory Farms or what?

    I’m guessing that Dan of #16 spends an average of 3.14 hours a day criticizing others to make himself feel superior. “So please don’t act all high and mighty smarter than mathematics.” He may know more than I do about numbers, but his language and social skills are a joke.

  25. AJ says:

    AnnJo (#10) -

    Unfortunately, in your example, the median numbers for that group are ALSO three legs, one wing, and half a beak! :-)

  26. Johanna says:

    Dan’s presentation may have been lacking, but he does have a point. Averages (and other statistical measures) don’t really lie – they just don’t tell the whole truth. (This isn’t necessarily a bad thing. In the case of the new home sizes, telling the whole truth would mean listing the size of each and every house that was built in 2008. You wouldn’t want to do that in a news article.)

    Where you run into trouble is when people take the averages to mean something more than they actually do. Maybe it’s because of grade inflation in schools (where most of the grades are A’s and B’s even though they still call C the “average”) that being “merely average,” let alone below average, is somehow inadequate. It’s not. If your house is smaller than the average of 2343 square feet, or even if it’s smaller than the median 2090 square feet, that doesn’t mean that there’s something wrong with it – it just means that a lot of new houses are bigger.

    Likewise, when high-sounding figures are quoted as the average wedding budget or the average amount parents spend to raise a child, that doesn’t mean you have to spend more than that amount or that there’s anything wrong with you if you don’t.

  27. Marsha says:

    Averages do not lie. Averages are only one statistice, and one that was never designed or intended to capture all relevant or interesting information.

    You could give people an average, a mean, and a standard deviation and they would still make flawed inferences.

  28. Doctor S says:

    Many numbers can be deceiving and your point shows that its probably good to look at the entire range and throw out the extreme values in most situation. I knew there was a reason I took that Applied Data Mining grad course!

  29. Dan says:

    @#24 Lenore and #26 Johanna

    Thanks for checking my attitude on that. You are correct, my presentation skills do lack. (on average they don’t though) :))))

  30. Georgia says:

    My example with numbers may not have to do with statistics, but it is often used. And I figured it out too late.

    When applying for Social Security, I came in 3 months early, as advised by SS. Well, my first check came less than 1 month later. The rep talked me into taking the SS benefits 3 months early. It would only be a loss of $15 per month. She said it would take me 6 years to make up for those 3 lost checks. I did the math when I got home and she was right.

    However, I decided to also do the math from my point of view. Forget the first 3 checks and just go for the regular amount. I tease that I intend to live to be 123. But, just suppose I made it only to 100 (which many people do nowadays). Using that time line, I have lost $5k. Always figure math both ways – the way of others and your way. Same figures, just different outcomes.

  31. Hank says:

    What an interesting way to look at the statistics! I never thought of it like that before. Thanks for the insight.

  32. Chad says:

    I think mainstream media uses averages (as opposed to other more telling stats.) due to two reasons; a) averages can be more sensational and b)most people understand the term “average”. I think the second reason plays a huge part in the overall picture. Lets face it, the “average” American is likely going to struggle with terms like median, mode, sigma, standard deviation, etc, etc but averages are straight forward math that most understand.

    A classic example of math V.S. public understanding is currently in the media. The SCIENTIFIC debate over cancer screening guidelines should be about the MATH. The scientists that developed these new guidelines just didn’t make them up, they analyzed the population and developed recommendation based on the overall statistics. Meanwhile, there are talk show hosts and other media speaking out against these guidelines with little understanding of the actual report results, i.e. the math behind the report. I have no issue with people disagreeing with the report results, but please have a scientific reason, i.e. “The study was flawed because the population size wasn’t statistically significant based on the amount of change the study was looking for.”

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