Misleading Averages

Many years ago, I attended a business conference where the keynote speaker sounded a note of caution about the word “average”. To illustrate his point, he told a joke about a man with one foot in a bucket of boiling water and the other foot in a bucket of freezing water. The man subjected to the excruciating extremes of temperature exclaimed that “on average” he felt comfortable.

For humour to be effective there has to be some truth present, which is why the joke’s punch-line drew laughter from the audience. The underlying message from the keynote speaker was clear: Averages can be very misleading. This is particularly the case where outliers can completely throw off an entire data set, rendering the average figure entirely meaningless.

For those of us in business selling good and services to consumers, we need to be careful about unwittingly providing commentary which might be considered “deceptive and misleading.” Quoting “averages” which distort reality could fall into that category.

For example, imagine there are 50 people in a room and each has assets totalling $500,000. This means the average assets per person is $500,000. Now imagine that one person leaves the room and is replaced by the world’s richest man – Elon Musk with an estimated net wealth of $350billion.

The inclusion of the Musk in the sample group causes the average assets per person to skyrocket by billions and billions of dollars – which is grossly misleading as only one is actually a billionaire. Yet the “average” wealth result gives the impression that all the people in the group are much better off than they really are.

It takes just one unrepresentative outlier to pull the average in their direction. This is why it’s said that averages conceal rather than reveal. Averages can obscure vital differences and mask important similarities. Just knowing the average of something does not tell the whole story.

Let’s take customer satisfaction surveys. One satisfied customer plus one dissatisfied customer does not make a “neutral” customer. You can’t average people and their attitudes but this has not stopped the misuse and misinterpretation of customer survey data.

As crazy as it sounds most people – statistically speaking – have more than the average number of legs. While the overwhelming majority of humans have two legs, some have one leg while others have none due to birth defects and/or accidents. When you mathematically calculate the average of every person on the planet, the resultant number is pulled down by those with less than two legs.

Allow me to provide a more pragmatic example of the flaw with averages. Take a household consisting of three generations of the one family – from young children to grandparents. If you add together the ages of the family members and divide by the number of members, this produces an average age that has absolutely no meaning whatsoever.

Another example which is closer to home for me is credit card debt in Australia. Statistically, the average credit card debt per household is $3,317. There are ten million households in Australia and 6.2 million of them have absolutely no credit card debt.

This makes the average credit card debt figure for all households meaningless. A more accurate measure would be to calculate the average credit card debt for the 3.8 million households with a credit card. This figure is much higher (and more realistic) at c$25,800.

Notwithstanding their shortcomings, people love averages. We humans are keen to know where we stand when measured against the average – average height, average weight, average income, average intelligence and so on. In doing so, we typically ignore just how wrong the picture is that averages paint of the world.

To be fair, in some instances the use of averages is perfectly valid and revealing. But this is only the case if what you’re trying to average is uniform and not skewed in any way. Beyond that, statistical averages have caused many a wise man to opine on their unreliability.

“Then there is the man who drowned crossing a stream with an average depth of six inches”. W.I.E. Gates

“Facts are stubborn things, but statistics are pliable”. Mark Twain

“There are three types of lies – lies, damn lies and statistics”. Benjamin Disraeli

Let me end with my own statement of the blindingly obvious:

“Our knowledge of averages is below average”.

All food for thought!