# Honey, I statistically shrunk the kids!

Statistics have value if interpreted correctly.

But we all know statistics can be manipulated as well. You can report statistics that are 100% true, yet interpret them to provide a misleading, or often opposite conclusion than the truth.

Here is a common statistical interpretation error:

A couple has three kids. One is 2 feet tall, one is 3 feet tall, and one is 4 feet tall.

The father, a statistician, makes note that 24 + 36 + 48 = 108, so he realizes his kids are an average of 36 inches, or 3 feet in height ( 108 / 3 ).

The next year, the kids have each grown 4 inches, and they have a new baby, who is 20 inches in height.

Now, the father calculates that 20 + 28 + 40 + 52 = 140 inches, and 140 / 4 =  35.

What??!?

So in one year, his kids have gone from an average of 36 inches to an average of 35 inches!

The father calls the doctor in a panic, yelling “The kids are shrinking! The kids are shrinking!”

The truth is, that the kids are not actually shrinking. The sample has changed.

Concluding that their kids have shrunk an average of 1/4″ each is an invalid way to explain the drop from 36 to 35 inches in their kids’ average height.

The true interpretation is, that because of the addition of a new baby that is shorter than the rest, the average height statistic has been skewed. The truth is that all kids are actually growing in height.

This is the invalid method used by every “rich get richer, poor get poorer” study ever done. The study does not follow individual households (as the study I cite here does), and makes the false assumption that rich and poor people are the same people over a span of time (which my article shows is usually false).