## How small is too small? (Part 2 of 3)

— Blog Post — 1 min read

As I mentioned yesterday, today’s post is about how body sizes at different ages vary. That is—the graph of the average z-scores that you saw yesterday doesn’t tell the whole story. Not every child is at the average. Indeed, many of them are doing a lot worse.

The graph below show height for age, again computed from the National Family Health Survey. Except this time, instead of plotting the average height for age z-score at different ages, I’ve plotted the 95th, 75th, 50th, 25th and 5th percentile height for age z-scores. [The box plot wasn’t working well because I couldn’t figure out how to properly label the axes in Stata. This picture gives the same idea.]

Once you’ve seen the graph of the averages, this graph seems fairly intuitive. The plot of the median (the 50th percentile) is pretty close to the plot of the average, and the 5th and 95th percentile kids are about equidistant from the 50th percentile.

But when we stop to think of what this means for the shortest kids, we realize that the average, can seem optimistic. Let’s take the three year olds. The average three year old in the healthy reference population is 95 centimeters—3 feet 1 inch—tall. A three year old with a z-score of -2 is 87.4 centimeters—about 2 feet 10 inches—tall. So, the average 3 year old in India is about 2 feet 10 inches. But the 3 year olds at the 5th percentile in India have a z-score of -4.25, meaning that they are only 78 centimeters—2 feet 6.5 inches—tall. 2 feet 6.5 inches is the average height of a 16 month old baby in the healthy reference population!

While it is true that small size, related to poor diets and lots of disease, is a problem for children of all socioeconomic groups in India, I can’t help but feel particularly sobered today by thinking about the children at the 5th percentile…3 year olds who are so small that their height would suggest that they are less than half their age.