Picture a jar full of jelly beans. I pull a jelly bean out of the jar. It’s red, so I declare that all of the jelly beans in the jar must be red. You quickly point out my logical error; the fact that one jelly bean is red doesn’t mean that all of them are. This is a straightforward example of an unrepresentative sample, a common logical flaw in which an argument incorrectly assumes that a certain sample group provides sufficient evidence to draw conclusions about another group.
Of course, the test-makers are adept at making this error trickier to spot than a single red jelly bean, so let’s take a look at some other examples.
It has long been assumed that snowboarding is a significantly more dangerous Olympic sport than skiing, but a 2006 study performed at the Winter Olympics in Torino demonstrates that there is no such disparity in risk. Of the very few injuries recorded at these Olympics, there were an equal number of snowboarders and skiers.
Here we have an unrepresentative sample that is too small or limited to represent the group about which the argument makes a conclusion. This is the same basic logic as the jar of jelly beans; the fact that injuries were equal among skiers and snowboarders in one particular Olympics is not enough for us to conclude that the sports are equally safe. Perhaps the Torino Olympics are anomalous when compared to other years, and snowboarders experienced a greater number of injuries than skiers during every other Olympics.
Samples aren’t always unrepresentative simply because they are too small or limited. They can also be unrepresentative if they differ in a significant way from the group about which the author makes a conclusion. Here’s an example:
The marketing department at a high-end fashion company was looking to boost circulation of its product. One of the managers had recently seen a study citing a rise in sales at grocery stores in response to advertisements placed by these businesses in the local free newspaper. The manager suggested that the marketing department place full-page advertisements in the local free paper in order to increase sales.
The manager mentioned in the argument assumes that a marketing strategy that has been successful for grocery stores will also work for a high-end fashion company. However, what if the customers who make enough money to buy high-end fashions don’t read the local free newspaper? They won’t see the advertisements, so the strategy won’t work to increase sales. Grocery stores differ significantly from high-end fashion companies in things like price point, product, and target market, so one cannot be said to sufficiently represent the other.
Unrepresentative samples appear often in assumption and logical flaw questions, so any time a conclusion is based on a certain sample, check to make sure that the sample is large enough and similar enough to sufficiently represent the group in question. Once you master these question types, treat yourself to a jelly bean or two – the red ones are delicious!