The smallest girl in the world

Question

When my daughter was born, she was pretty small: 5lb 14oz. We were told that put her at exactly second centile for non-prem girls.

At one point, I asked the doctor whether we should be worried, and she said no, not as long as she stayed on the second centile track. Then she said something rather silly:

We don't worry about babies unless they drop off by two centiles.

Obviously that doesn't make much sense as a general principle: dropping from 3rd to 1st ought to be much more alarming than dropping from 99th to 97th.

But what I'm interested to know is: what would that rule have meant, if strictly applied to my daughter? I can think of four possibilities:

1. She'd have to shrink to a point.
2. She'd have to drop to being the smallest girl in the world.
3. It's meaningless/undefined.
4. There's not enough information given to answer the question.

Which is it?

Answer 1

Percentiles are usually labelled by their lower bound. e.g. a quantity in the 99-th percentile lies somewhere between the 99% and 100% mark in the list of all possible quantities.

A quantity lying between the 0% and 1% mark, therefore, would be the 0-th percentile.

As an aside:

Obviously that doesn't make much sense as a general principle: dropping from 3rd to 1st ought to be much more alarming than dropping from 99th to 97th.

You make presumptions about the normal development of a child that probably aren't warranted: judging from your report of the doctor's comment, healthy children tend to grow at a rather standard pace; jumping several centiles could very well be a good indicator that there is something may be wrong with the child; you really should ask about that someplace where they actually know about this stuff.