In 1945, two sculptures meant to represent the average man and woman in the United States went on exhibit at the American Museum of Natural History.

Based on measurements taken from tens of thousands of young men and women, they were called Norma and Normman.

That same year, a contest launched to find a living embodiment of Norma.

Normal is often used as a synonym for "typical," "expected," or even "correct."

By that logic, most people should fit the description of normal.

And yet, not one of almost 4,000 women who participated in the contest matched Norma, the supposedly "normal" woman.

This puzzle isn't unique to Norma and Normman, either—time and time again, so-called normal descriptions of our bodies, minds, and perceptions have turned out to match almost no one.

And yet, a lot of the world is constructed around a foundation of normalcy.

So what does normal actually mean—and should we be relying on it so much?

In statistics, a normal distribution describes a set of values that fall along a bell curve.

The average, or mean, of all the values is at the very center, and most other values fall within the hump of the bell.

These curves can be tall, with most values inside a narrow range, or long and flat, with only a slight bias towards the average.

What makes the distribution normal is that it follows this curved shape.

Normal doesn't describe a single data point, but a pattern of diversity.

Many human traits, like height, follow a normal distribution.

Some people are very tall or very short, but most people fall close to the overall average.

Outside of statistics, normal often refers to an average—like the single number pulled from the fattest part of the bell curve—that eliminates all the nuance of the normal distribution.

Norma and Norman's proportions came from such averages.

Applied to individuals, whether someone is considered normal usually depends on how closely they hew to this average.

At best, such definitions of normal fail to capture variation.

But oftentimes, our calculations of normal are even more flawed.

Take the BMI— or Body Mass Index.

BMI is a measure of weight relative to height, with different ratios falling into "underweight," "normal weight," "overweight," and "obese" ranges.

Generally, only BMIs that correspond to normal weight are considered healthy.

But BMI is not always an accurate predictor of health, or even of what's a healthy weight.

BMI doesn't take into account body fat percentage, body fat distribution, levels of physical activity, or blood pressure.

And yet, those who fall outside the so-called normal range are commonly advised that losing or gaining weight will improve their health.

When we apply a standard of normal to all of humanity that's based on data from a non-representative slice,

we're not just choosing one point on the distribution, we're choosing it from the wrong distribution.

A lot of behavior science research draws from samples that are pretty WEIRD—meaning Western, educated, industrialized, rich, and democratic.

These features can skew norms even in research that doesn't have an obvious link to them.

Take the famed Muller-Lyer optical illusion: it's normal to think one of the two lines is longer, when they're actually the same length.

At least, it is if you're an American undergraduate.

A team of anthropologists and psychologists found other demographic groups were much less susceptible—members of the San people of the Kalahari weren't susceptible to the illusion at all.

When these limited or inaccurate definitions of normal are used to make decisions that impact people's lives, they can do real harm.

Historically, such concepts of normal have been hugely influential.

The Eugenics Movement of the early 20th century weaponized the concept of normal, using it to justify exclusion, violence, and even extermination of those deemed not normal.

To this day, people are often targeted and discriminated against on the basis of disabilities, mental health issues, sexual orientations, gender identities, and other features deemed "not normal."

But the reality is that the differences in our bodies, minds, perceptions, and ideas about the world around us—in short, diversity— is the true normal.

And speaking of deeply flawed system of measurement, how much do you know about the dark history of IQ tests? Learn more with this video.

Or get the latest on an important debate: Should we get rid of standardized testing?