Tag Archives: mean

Finding the mean, median, and modal Walmart shopper

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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.

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

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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

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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.

“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.

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.

An emerging portrait of emerging adults in the news, part 2

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In recent weeks, a number of studies have been reported on that discuss the beliefs and behaviors of the younger generation, those who are now between high school and age 30 (an age group that could also be labeled “emerging adults”). In a three-part series, I want to highlight three of these studies because they not only suggest what this group is doing but also hints at the consequences. (Find part one here.)

In Sunday’s edition of the Chicago Tribune, there was a story citing research that shows emerging adults are more tolerant than previous generations on issues like intermarriage, gay marriage, other races, and immigration. Yet, at the same time, there is also research suggesting levels of empathy among college students are down about 40% compared to the 1970s:

“Millennials, A Portrait of Generation Next,” an extensive study of teens and 20-somethings released earlier this year, showed that members of the Millennial Generation, generally born between 1981 and 2000, are “more racially tolerant than their elders.”

More than two decades of Pew Research surveys confirm that assessment.

“In their views about interracial dating, for example, Millennials are the most open to change of any generation,” the report states.

The study goes on to report that nearly 6 in 10 Millennials say immigrants strengthen the country, compared with 43 percent of adults ages 30 and older…

The problem is that tolerance doesn’t necessarily mean understanding, researchers say. Adults working with teens say they see an unsettling strain of desensitivity among young people.

In May, University of Michigan’s Institute for Social Research issued a report on an analysis of 72 studies on the empathy of nearly 14,000 college students between 1979 and 2009. The result: Today’s college students are about 40 percent lower in empathy than students two or three decades earlier.

The researchers suggested that disheartening trend may have to do with numbness created by violent video games, an abundance of online friends and an intensely competitive emphasis on success, among other factors.

This is a very interesting conclusion: the younger generation is more tolerant but less understanding and empathetic. So what exactly does this tolerance look like? The lack of empathy, in particular, is interesting as it is another step beyond tolerance. Empathy is the ability to understand and take on the feelings and perspectives of others. Is tolerance the end goal or is there more that we should be striving for as a society?

This conundrum reminds me of Jesus’ Sermon on the Mount, the current topic of our Sunday School class. In verse after verse, Jesus suggests that Christians aren’t just supposed to put up with people: “loving your neighbor” means taking an extra step toward people, bringing reconciliation, peace, and blessings to other rather than just letting them be or letting them pursue their rights in their own space. Loving people means putting them above yourself, something beyond both tolerance and empathy.

One outcome suggested by this story is a meanness or harshness among high schools. Teenagers understand about respecting difference but this doesn’t translate as well into personal interactions where being mean is seen as being cool.

Another possible outcome is living alone, keeping people at a distance. I will consider this in part three of this series.