Tuesday, 9 October 2012

Tune in Tomorrow, When We're Gonna Do *FRACTIONS*

Came across an interesting article yesterday in The Economist.  The authors were commenting on a recent study by economists at the University of Miami that discovered another reason why mathematics are important.

It turns out, the 'average' American's inability to grasp concepts around fractions and proportions, added to the lure of "more," yields poor choices, at least when it comes to the allocation of economic resources (i.e., our money).

The study of 600 shoppers asked for opinions on the best "bargain" when confronted with various options.

Overwhelmingly, when given the choice of the same amount of product for less vs. more product for the same price, the shoppers opted for more, even when the better bargain was the latter.

As an example, shoppers were given the choice of product A, either at a 33% discount, or 33% additional product at no additional cost.  The choice overwhelmingly was for "more stuff for free," with shoppers indicating that the two 'bargains' offer the same value.

Well, a quick look at the maths makes it clear that the better choice - economically speaking at least - is to opt for the discount.  Quickly think of a 10 ounce bottle of shampoo, for $1.  If you get the same shampoo at a 33% reduction, you will pay 67 cents for 10 ounces.  That's 6.7 cents per ounce.

On the other hand, if you opt for "more stuff," you get 13.3 ounces for one dollar, or 7.5 cents per ounce.  As an aside, for the two to be equivalent, the additional "free" product would have to be 50% more.

In another experiment, shoppers were asked to compare two scenarios, one where a product was discounted 40%, and another, where a product was discounted 25%, and then given a "super" additional discount of 20% on top.

Again, overwhelmingly, the shoppers thought that option B was superior.  The classic, grade eight algebra fallacy that 25% plus 20% must be 45%.

In this case, the two scenarios are equal.

Think of the same bottle of shampoo, offered at $1.  A single, 40 per cent discount takes the price to 60 cents.  Under the second scenario, the initial reduction takes the price to 75 cents, with an additional 20 per cent reduction taking the price to, once again, 60 cents.

We tend to 'fall' for spurious "buy one, get one free," or "additional discount taken at register" offers, and ignore what our high school maths teachers taught us about fractions and how to multiply and add them.

When in doubt, one can of course ignore the math test, and instead just rely on reading - at grocery stores, virtually all products listed will print the unit price on a small tag on the shelf.  When in doubt, just read.

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