Finding the mean, median, and modal Walmart shopper

An analytics firm describes the “typical” Walmart shopper:

Photo by Michael Burrows on Pexels.com

Numerator found that Walmart’s typical shopper in the US is a white woman between 55 and 64 years old, who is married and living in the suburbs of the Southeast. She typically has an undergraduate degree and earns about $80,000 per year.

She visits Walmart at least once per week — about 63 trips per year — and picks up 13 products for a total cost of about $54 per trip. 13.5% of her spending takes place at Walmart, while she spends about 11% at Amazon.

Her primary shopping categories in-store are groceries, including chicken, fruit, snacks and sweets, but she also gets a lot of fast food. Her favorite five brands at Walmart are Turkey Knob, Cheetos, Betty Crocker, Dole, and Tyson.

I am always looking for examples to help illustrate the differences between the three primary measures of central tendency: mean, median, and mode. When an article or report says something is “typical,” what exactly do they mean? Here is my guess at which data above is which measure of central tendency:

-mean: age, education level, visits to Walmart, money spent per trip

-median: income

-mode: race/ethnicity, marital status, place of residence, what is purchased

Some of these are harder to guess or do not fit these three options well. For example, is the $54 per visit a mean or median? Or, the five favorite brands are not a singular mode and they may lead the list of brands but not actually comprise that much of the total percent of purchases.

Additionally, it would be interesting to add measures of variability. How much variation is there in the age and education level of Walmart shoppers? I would guess the company wants to know more about the $54 spent per trip; how many spend more and what could be done to increase the number of people who spend more? Throw in a standard deviation or some other measure of dispersion and the numbers above become much more interesting.

In the end, the report above does not mean that someone visiting a Walmart will find most shoppers fit that profile. The measures of central tendency here tell us something but using multiple measures plus some measures of variability would provide more in terms of revealing who is at Walmart.

The modal age of racial/ethnic groups in the United States

There is a big age difference in the most common age among racial and ethnic groups in the United States – particularly compared to the median.

In U.S., most common age for whites is much older than for minorities

 

 

 

 

There were more 27-year-olds in the United States than people of any other age in 2018. But for white Americans, the most common age was 58, according to a Pew Research Center analysis of Census Bureau data.

In the histogram above, which shows the total number of Americans of each age last year, non-Hispanic whites tend to skew toward the older end of the spectrum (more to the right), while racial and ethnic minority groups – who include everyone except single-race non-Hispanic whites – skew younger (more to the left).

The most common age was 11 for Hispanics, 27 for blacks and 29 for Asians as of last July, the latest estimates available. Americans of two or more races were by far the youngest racial or ethnic group in the Census Bureau data, with a most common age of just 3 years old. Among all racial and ethnic minorities, the most common age was 27…

Non-Hispanic whites constituted a majority (60%) of the U.S. population in 2018, and they were also the oldest of any racial or ethnic group as measured by median age – a different statistic than most common age (mode). Whites had a median age of 44, meaning that if you lined up all whites in the U.S. from youngest to oldest, the person in the middle would be 44 years old. This compares with a median age of just 31 for minorities and 38 for the U.S. population overall.

The paragraphs above provide multiple pieces of information that explain the distribution displayed above:

-The different groups have different skews, suggesting these are not even distributions.

-The mode is much higher for whites.

-The median agrees with the conclusion from the mode – whites are on average older – but the gap between whites and other groups drops.

All three pieces of information could inform the headline but Pew chose to go with the mode. Is this with the intent of suggesting large age differences among the groups?

Median college debt under $17k

While college debt as a whole hits record levels – over $1.3 trillion – the median debt is much more reasonable:

The median amount was nearly $17,000, but nearly 20 percent of those households owed more than $50,000.

I would suggest a disproportionate amount of media attention goes to college students at highly ranked or high status institutions that amass a lot of debt while most college students have more manageable amounts of debt. Of course, any debt may be difficult to pay back but there is a big difference between the median – $15k – versus the 80th percentile – $50k.

If debt was such an issue, why do Americans keep going to the more expensive institutions? Are too many students and families unnecessarily striving for “the best” when a cheaper yet good education would likely do?

Average full-time work week is 47 hours; median is around 40 hours

A number of headlines have screamed about a recent Gallup finding that the average American full-time worker works 47 hours a week. Yet, the median appears to conform to the typical 40-hour work week:

Adults employed full time in the U.S. report working an average of 47 hours per week, almost a full workday longer than what a standard five-day, 9-to-5 schedule entails. In fact, half of all full-time workers indicate they typically work more than 40 hours, and nearly four in 10 say they work at least 50 hours.

Average Hours Worked by Full-Time U.S. Workers, Aged 18+

 

 

 

 

 

 

 

 

 

The 40-hour workweek is widely regarded as the standard for full-time employment, and many federal employment laws — including the Affordable Care Act, or “Obamacare” — use this threshold to define what a full-time employee is. However, barely four in 10 full-time workers in the U.S. indicate they work precisely this much. The hefty proportion who tell Gallup they typically log more than 40 hours each week push the average number of hours worked up to 47. Only 8% of full-time employees claim to work less than 40 hours.

These findings are based on data from Gallup’s annual Work and Education Survey. The combined sample for 2013 and 2014 includes 1,271 adults, aged 18 and older, who are employed full time.

Is the average the best measure here? This is a classic case where the median and mean give you different conclusions. The median tells you that not much has changed from the standard: half of full-time workers work 40 hours or less. The average, on the other hand, is pulled up by those people working 50+ hours. As the Gallup analysis goes on, it notes that there is a difference between salaried and hourly employees with salaried workers working more of those 40+ hour weeks. These salaried workers are likely white-collar and professional workers, people who may be working more but likely have more credentials, are getting paid more, and have higher-status jobs.

So, perhaps the headlines might be more accurate by saying “Salaried full-time workers have higher [47? 50?] hour work week.”

Average American net worth #4 in the world; median net worth #19

In another case of mean versus median, looking at the average or median net worth of Americans leads to different conclusions:

Americans’ average wealth tops $301,000 per adult, enough to rank us fourth on the latest Credit Suisse Global Wealth report.

But that figure doesn’t tell you how the middle class American is doing.

Americans’ median wealth is a mere $44,900 per adult — half have more, half have less. That’s only good enough for 19th place, below Japan, Canada, Australia and much of Western Europe…

Super rich Americans skew average wealth upwards. The U.S. has 42% of the world’s millionaires, and 49% of those with more than $50 million in assets.

Both figures are true but they tell very different stories. America at #4 or #19?

Some other interesting tidbits later in the article:

1. Homeownership helps other countries pass the U.S. in median wealth since some have higher rates of homeownership (like Ireland and Spain) and their housing markets didn’t experience such a bubble.

2. Americans can borrow money more easily than some. This means we might be able to get our hands on more but leads to more debt which subtracts from our net worth.

Methodological issues with the “average” American wedding costing $27,000

Recent news reports suggest the average American wedding costs $27,000. But, there may be some important methodological issues with this figure: selection bias and using an average rather than a median.

The first problem with the figure is what statisticians call selection bias. One of the most extensive surveys, and perhaps the most widely cited, is the “Real Weddings Study” conducted each year by TheKnot.com and WeddingChannel.com. (It’s the sole source for the Reuters and CNN Money stories, among others.) They survey some 20,000 brides per annum, an impressive figure. But all of them are drawn from the sites’ own online membership, surely a more gung-ho group than the brides who don’t sign up for wedding websites, let alone those who lack regular Internet access. Similarly, Brides magazine’s “American Wedding Study” draws solely from that glossy Condé Nast publication’s subscribers and website visitors. So before they do a single calculation, the big wedding studies have excluded the poorest and the most low-key couples from their samples. This isn’t intentional, but it skews the results nonetheless.

But an even bigger problem with the average wedding cost is right there in the phrase itself: the word “average.” You calculate an average, also known as a mean, by adding up all the figures in your sample and dividing by the number of respondents. So if you have 99 couples who spend $10,000 apiece, and just one ultra-wealthy couple splashes $1 million on a lavish Big Sur affair, your average wedding cost is almost $20,000—even though virtually everyone spent far less than that. What you want, if you’re trying to get an idea of what the typical couple spends, is not the average but the median. That’s the amount spent by the couple that’s right smack in the middle of all couples in terms of its spending. In the example above, the median is $10,000—a much better yardstick for any normal couple trying to figure out what they might need to spend.

Apologies to those for whom this is basic knowledge, but the distinction apparently eludes not only the media but some of the people responsible for the surveys. I asked Rebecca Dolgin, editor in chief of TheKnot.com, via email why the Real Weddings Study publishes the average cost but never the median. She began by making a valid point, which is that the study is not intended to give couples a barometer for how much they should spend but rather to give the industry a sense of how much couples are spending. More on that in a moment. But then she added, “If the average cost in a given area is, let’s say, $35,000, that’s just it—an average. Half of couples spend less than the average and half spend more.” No, no, no. Half of couples spend less than the median and half spend more.

When I pressed TheKnot.com on why they don’t just publish both figures, they told me they didn’t want to confuse people. To their credit, they did disclose the figure to me when I asked, but this number gets very little attention. Are you ready? In 2012, when the average wedding cost was $27,427, the median was $18,086. In 2011, when the average was $27,021, the median was $16,886. In Manhattan, where the widely reported average is $76,687, the median is $55,104. And in Alaska, where the average is $15,504, the median is a mere $8,440. In all cases, the proportion of couples who spent the “average” or more was actually a minority. And remember, we’re still talking only about the subset of couples who sign up for wedding websites and respond to their online surveys. The actual median is probably even lower.

These are common issues with figures reported in the media. Indeed, these are two questions the average reader should ask when seeing a statistic like the average cost of the wedding:

1. How was the data collected? If this journalist is correct about these wedding cost studies, then this data is likely very skewed. What we would want to see is a more representative sample of weddings rather than having subscribers or readers volunteer how much their wedding cost.

2. What statistic is reported? Confusing the mean and median is a big program and pops up with issues as varied as the average vs. median college debtthe average vs. median credit card debt, and the average vs. median square footage of new homes. This journalist is correct to point out that the media should know better and shouldn’t get the two confused. However, reporting a higher average with skewed data tends to make the number more sensationalistic. It also wouldn’t hurt to have more media consumers know the difference and adjust accordingly.

It sounds like the median wedding cost would likely be significantly lower than the $27,000 bandied about in the media if some basic methodological questions were asked.

Assessing “The Return of McMansions” in the NYT

Following up on the same data behind the CNN story on the McMansion comeback, the NYT looks more closely at the characteristics of new houses in 2012. Here is my summary:

-Housing starts were still down in 2012. Looking at the graph with housing start data since 1973 shows that the last few years have been quite different.

-The homes built in 2012 were bigger: the highest median square footage ever of 2,306 square feet, 41% of the houses were four or more bedrooms (a new record), and 30% of new houses had 3 or more bathrooms (also a new record).

My thoughts on this data:

1. This is not a big surprise. While housing starts are way down, wealthier Americans and others have still been able to buy large new homes. Again, Toll Brothers is doing just fine. On the other hand, the lower ends of the housing market are not doing well.

2. It is interesting again for people to pick up on the highest-ever median square footage for new houses. For years, journalists and others have looked at the average square footage which is bit down from its high several years ago. Perhaps the median is now alluring because it is at its highest point and therefore can be linked to McMansions and American excess?

3. More houses have more bedrooms and yet the average family size in the United States has decreased in recent decades and more Americans are now living alone. So what are these bedrooms being used for?

 

CNN says “McMansions are making a comeback” but the data is limited

CNN reports that McMansions just may be on the way back:

During the past three years, the average size of new homes has grown significantly, according to a Census Bureau report released Monday. In 2012, the median home in the U.S. hit an all-time record of 2,306 square feet, up 8% from 2009.

During the recession, Americans downsized and the average new home shrunk in size by 6% over two years to 2,135 square feet. At the time, many industry experts said the days of the McMansion were over.

The shrinkage was supposed to indicate that a new era had begun, with young buyers seeking to live closer to urban cores and settling for smaller places and baby boomers downsizing after their kids had flown the nest.

But it wasn’t that consumers wanted less space, many just couldn’t afford more, said Jeffry Roos, a regional president for home builder Lennar. And now that the economy is improving, they’re demanding bigger homes again, he said.

This is what I suspected might happen: once the housing market picked up again, some Americans would go back to buying bigger houses. But, this article has a few problems as it relies on (1) the median home size and (2) talking to several large builders.

Regarding home size: the figures cited more often is the average home size. The average size for new houses went from roughly 900 square feet in 1950 to nearly 2,500 in the mid-2000s. The median home size might be more accurate as the extra big homes can’t skew the data as much but the average is used more often. Also, the median hasn’t changed all that much in the last few years – this is only a difference of 150 square feet, a 12×12 room. Why can’t we see figure about the number of big homes that have or have not been built rather than relying on these overall figures that are a snapshot of a varied housing industry?

Relying on just a few large builders also does not reveal the big picture. The builders cited, particularly Toll Brothers, are big players but the housing market has a lot of different builders and developers. Overall, how are lots of different builders feeling about big houses? Are they actually building these bigger houses? What do real estate experts say? The news for Toll Brothers has looked good recently but there is more to the big house market than just Toll Brothers.

This seems like an article that would benefit from better data and also may not really be able to be written until some more time has passed and the trend is more clear. In the meantime, simply invoking the term McMansion and discussing a possible trend is apparently enough…

UPDATE 6/5/13: As the CNN story is repeated across the web, there is some confusion. For example, look at how this retelling mixes the idea of an average or median:

A new Census Bureau report says the average size of a new home has grown eight percent in the last three years, up to a record 2,300 sq. ft. in 2012…

According to the National Association of Homebuilders, buyers prefer a median home size of just over 2,200 feet, in line with the Census average.

Two different figures for the “middle” size mean two different things…

“The average Australian is a suburban Frankenstein”?

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

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).