Fun with Statistics ~ Mean vs. Median using Fructose as an example

A bit of a ramble {grin}

Lately, all the buzz is on fructose as being the root of all evil.  All of a sudden, all fructose from all sources is suspect for ills ranging from obesity to hang nails!  Many studies involve doses of 50g isolated at one time or up to 200g as part of the diet during the day.  Fructose consumption is often reported to average ~50g/day in Western diets.  And yet when I think what a "moderate" fructose consumption would involve, I just don't see lots of people around me eating like that.

I believe that using the mean (average) as a measure of center for consumption is misleading and a better measure of center would be the median consumption.

For those not fluent in statistics, the mean (average) and the median (physical midpoint separating the bottom 50% of a population from the top 50%) are different ways to represent the "center" of a data set.   In most applications, the mean is the number reported (usually along with the standard deviation to indicate variability) -- it is considered the most rigorous measure as each data value is included in the calculation and weighted equally.  However when you have a situation where the propensity for outliers is greater at one extreme or the other, and/or one extreme is bounded while the other is not, general practice is to report the median.

Consider household incomes that are reported periodically based on IRS data -- almost always, the median household income is the reported value.  Why?  Because the least income one could have reported to the IRS is zero (or even a few thousand), but there's no theoretical limit to the high end of income.  All you need are a few outliers to make 10X, 100X, 1000X or even more to really throw an average.  Let's say you have 9 households, one each making 10K, 20K, etc up to 90K.  The mean income = median income = 50K.  Now let's say the highest earner made just double 90K = 180K  now the mean = 60K while the median remains 50K ... not too bad, but we see that now 5 households make less than the average while only 3 make more.  If just the highest earner makes 900K, the median remains 50K while the mean is now 140K!!  Only one household earns substantially more than the average, while the other 8 make substantially less.  Leaving Mr&Mrs BigBucks at 900K, what happens if our low earners make zero?  If 10K goes to zero the median stays the same, the mean is lowered an inconsequential amount to just under 139K; if 20K also goes to zero, the mean is only lowered to around 136.5K.  Now this is a small data set, but I think you can see the picture.

By my calculations, Coke contains ~21.5 g fructose per 12 oz. can.  Let's say you have 9 people consuming 1 can through 9 cans/day.  The mean consumption would equal the median would equal 107.5g/day.  Is this how Westerners consume Coke?  I'm thinking not so much.  There are a good number of people who either don't drink soda or drink sugar free versions.  We would have to reduce the bottom 3 people to zero to get the mean down below 100g, but up the highest consumer to 15 cans/day (what Jimmy Moore claims he drank prior to going LC) and the mean is back to 107.5.  Two more numbers games -- let's say our 9 people consume on average 0,0,.5,.5,1,1,2,2,12 this amounts to an average fructose consumption just under 50g/day, but a median consumption of a reasonable approx 20g/day.  Moreover, only 2 consumers exceed average consumption while 7 consume quite a bit less.    Or we could have large numbers at the extremes -- the lowest 3 consume no fructose, the highest 3 consume 150 g/day and the remaining 3 somewhere in the middle.  We can easily get at the same mean (and probably the same median) but NEITHER statistic reflects what is really going on in such a society.  I tend to think this is typical of Americans when it comes to all sorts of dietary consumption.  We probably have some that eat a ton of something and just as many that rarely if ever touch the stuff.

No doubt there are fructose outliers in our society.  Those who eat candy like ... well ... candy!  And those that drink a large portion of their daily calories.   But do we really know a lot of folks like this?  Maybe I'm the outlier here, but nobody in my family drinks regular soda, juice or sugary drinks on any sort of regular basis.  Same goes for candy consumption.  When I snoop a peek into the shopping carts at the market, I'll occasionally see a 2L bottle or two or a case of cans along side what appears to be food for the week for a family.  IOW, even if the shopping cart pusher is consuming all the soda it would amount to a can or two a day.   Where I see large numbers of bottles or cans piled into a cart it is usually diet soda or water.  Yes there are some people having ginormous sugary coffees at Starbucks daily, but I've never had one and most of the people I know drink coffee w/o sugar, with AS, or with a packet of sugar (2.5g fructose per).

The mean consumption is easier to estimate based on food supply data, etc.  However the median is clearly a better measure of center here.

So where am I going here?

One of the stats looked at for fructose is comparing average consumption of various cultures.  We now have a threshold derived from this comparison of around 50g/day -- below that we see less disease, obesity, etc. and above that we see more.  But this has caused that value to be adopted as some "safe" level of consumption to avoid issues.   However, the bulk of a society averaging, say, 30g/day might just be consuming even less than that if there is a segment of over-consumers.  This can be interpreted two ways -- either the "safe" level of fructose consumption is considerably lower than the 50g number, or average consumption values for cultures are of very limited use in establishing fructose consumption recs.  I tend to be in the group that believes the latter.  It's like the fat consumption meta study that came out several months ago.

When it comes to the optimal human diet for health and weight management, I don't put much stock into these cultural comparisons other than to look for lifestyle trends.  Why?  Especially the more isolated or traditional cultures tend to consume "ethnic" foods specific to the region and their society has adapted to this over thousands of years.   I'm much more swayed by well controlled studies where actual hormone, lipid, glucose, etc. levels are measured.  Unfortunately, we can't have any such studies that are truly considered long term for the purposes of maximizing health, but then the next best thing is the retrospective meta studies that looks for correlations between behaviors and markers etc.  Not perfect, but still better than comparing cultures as a whole because individual values are used.  If summary data from a group of studies is compared, this is again of limited value.

I tend to think if one million Americans were randomly selected from all corners of the country (say selecting equal numbers from each Congressional district) and monitored consumption for a month, the "average" American diet would differ considerably from both the food pyramid, what we consider the SAD/"Western" diet to be, etc.   So when they compare disease rates for the US to other countries, or even to the US a century ago, there's not much value to this in determining what the optimal diet should consist of.

Yep ... a ramble :)