Statistics about Body Height

Statistics, you just got to love them.

Often tall people ask questions like: "Why do those designers make products too small?" "I'm a 6'1" American famale, am I really that tall?" "Are Asian males shorter than western famales?"
Actually these questions are quite easy to answer, when you have got the data and the right statistical techniques.

So I worked myself through some books and got my toolkit ready. Get ready for some statistical wizardry.

You can read about four topics:

I start with the most simple data and gradually add more statistical techniques to produce more advanced results.

Here is the most simple statistical way of describing a population: The mathematical average. You measure a lot of random selected people (1,000 or more), add all the heights, and divide them by the number of people you measured. Thus you get the (mathematical) average height. Any person that is born is expected to grow up to around this height. Random disturbances (diseases, malnutrition) or structural disturbances (genes-set) make that people don't reach or grow past this average.

Average Heights of People:

And thus we find the answer to the question: "Are Asian males shorter than Western famales?" As you can see in the table, Asian males are on average just a bit taller than USA and German famales, but the difference is only about 2.5 cm (1"). It is possible to calculate the chance for a random famale of these countries to meet a random, but shorter Asian male. This chance is about 45%. Thus the impression exist that Asian men are shorter. The table also shows that the Dutch famale really is taller than the average Japanese male.

People differ in height, just like I and my friend Jitka differ 40 cm (16").

Statisticians get really excited when they know or have calculated the variation of a population: Suddenly a whole world of confidence intervals, reliability and chances opens up.
I'll first try to tell you what statistical variation is.

In this picture above here you can see what happens when you start measuring people. Every person is different and has a different height. All the different measured heights are depicted here as arrows. Most people fall near the average and some fall short of it or are much taller.
When you divide the scale into classes and you sum up the number of people that fall into a class, you can make a bar-chart. Through the ends of the bars you can draw a 'continues distribution function', as it is called. This distribution function is fitted to the bar chart with use of a technique called 'regression'. As a function for fitting usually the bell-shaped 'Normal Distribution' is chosen. This Normal Distribution Function is defined by two parameters, its average, the position of the top, and the variation, which defines the width of the bell-shape. A high variation makes it wider and means that there are a lot of people that are far from the average, very tall or very short.

The next step in describing a population is trying to catch the big majority, for instance 95% of the people, within a certain range. This is possible using a feature of the distribution chart, namely that the surface under the function equals 1.

When we want to find the limits we can (mathematically) shade a certain percentage of the chart and find the outer borders. For instance: We want to know how tall 95% of the famales in Japan is. It turns out that the lower border and upper border of the chart of which 0.95 is shaded is 145.0 (4'9" 1/8) 160.8 (5'3" 3/8). And thus we conclude that 95% of the famales in Japan is between 1m45 and 1m61 tall.
When you want to include a greater portion of people into your interval, more very short and very tall people are added and the interval becomes bigger. You can see this when you look at the interval 99% interval for Japanese famales is 141.8 (4'7" 7/8) 164.2 (5'4" 5/8). The tallest person in this interval is 3,2 cm (1 1/4 inch) taller.
Why not include 100% of the people into the interval? The answer to this question is one of the statistical curiosities: The left and right tails of the function go to infinity, meaning that there exist people which are for instance 1cm or 16m in size. (The chance of finding such person is as big as being hit by a meteorite though.) Thus the answer to the question "How tall is a random person, with 100% certainty?" is answered by a statistician with: "Somewhere between 0 and 100m (0 and 300 feet), though there is a small chance that..."

Now we ask ourselves the question: How tall is 95%, 97.5% and 99% of the population in the USA, Germany, Japan and the Netherlands? You can find the answers in the tables below here:

Confidence Intervals for Body Height

And now we can also answer the question: "Why do those designers make products too small?". Some products are to accommodate a range of people in different sizes (cars, beds, chairs in planes and busses) or are specially made to fit people with a certain size (shoes, clothes).
Manufacturers make these products in such a way that they can accommodate the majority of people around. Making a product for a too big range of people or making too big range of sizes of one product will cost too much, because of extra material and moulds and since the extra size is not always needed and won't sell.
And thus car designers for instance reason: We can make a car that suits the shortest famale and tallest male in 99% of the cases. Using the table above here for USA people we can see the car thus needs to be able to accommodate a person between 147.6 (4'10" 1/8) and 192.0 (6'3" 5/8). If this car would be exported to The Netherlands it would be too small for the tall people, since the tallest male in the 99% interval is 200.0 cm (6'6" 3/4).
Although this looks far fetched, it did happen and still happens today. A good example is the old Honda CRX, a small Japanese sports car which turned out to be too small for most of the Western buyers. Braun, a German electric shaver producer who exported his products to Japan and found out they were too big too fit in the Asian hands.

Because most manufacturers choose to limit their products to this range, or because still people turn out to be unexpectedly tall, products won't fit sometimes. Having things tailor-made is often the best solution.

Last and most difficult thing to calculate: The partition of people that are over a certain height.
With this data you can answer a whole range of questions.

Before you dive into the tables I might explain what the numbers mean. On the left there are the heights you are looking for. In the cells under the names of the different countries there are two numbers, one of which is smaller than 1 and one of which is higher than 1.

Because the Japanese are so much shorter I had to make a separate table:

So now we can answer the question: "I'm a 6'1" American famale, am I really that tall?". When you look in the table you see for USA Famale 1m85 (6'1"):
Partition of people taller than her: 0.0002.
Number of people shorter than her: 5,000
Since 99,98% of the famale population in the USA is shorter than her, you might conclude that indeed she is 'really that tall'.

Another person posted this question in alt.support.tall:

Very tall According to "JC Penney".

In their catalogue "Especially for talls." there is written:
Tall womem......... are 5.8 (1m73) - 5.11 (1m80)
Ultra Tall womem... are 5.11 1/2 (1m82) to 6.2 (1m88).

I'm 6.3 (1m91) so I wonder.... what am I classified as??? Super Ultra Tall????
Angie

Let's have a look at the table again: USA Famales 6'3" (1m91): It says 'very rare'. This means that there is less than one famale in 10,000 that grows to or past this height. This is even so in Germany, but in the Netherlands there still is a small number, namely one in 1,429 famales, between 18 and 30 years, that has grown past this height.
Congratulations Angie, you indeed are Super Ultra Tall. ;-)

This is the same calculation as above here 'How many people are above a certain height', but calculated backwards in some sense.
Here we ask ourselves: Who are the upper 0,1 0,01 or 0,001 % of the population when it comes to height?

As explained under variation: It is possible to calculate these 'critical values' using mathematical shading:

But now we shade 99,9 99,99 and 99,999% of the chart and ask ourselves how tall you need to be, to still fall in the not-shaped area. Or, in other words, to be taller than 99,9 99,99 or 99,999% of the population. Statisticians call these values critical values, because when measuring, they appear only very few times.

In the table below here you can see the critical values for males and famales in the USA, Germany, Japan and the Netherlands. Example: USA Males 5000: 200.7 (6'7"). This means that, for the USA, one in 5000 males (0.02%) is above 200.7cm (6'7").

Critical Values for Maximum Height for People in Different Countries

I collected data for the United States of America, Germany, Japan from Grandjean's book "Fitting the Task to the Man", 1987 and for the Netherlands from the Central Bureau for Statistics, the year 1996, demography. The average of Japan is representative for most Asian countries, as is German for most north-west European countries.
The people of the Netherlands are the tallest in the world. Of them, I collected averages for young adults age 18-30 years.

Data Chart
Average Height (mm); Standard deviation (mm)

With help from this chart and the table for Z-values of the Normal Distribution you can calculate all tables above here.

I know this is a whole lot of data, but still I hope that, together with the explanations, I cleared up some questions about being tall in relation to others in the population.
When you feel you still have unanswered questions, or when you want to know how many people are shorter than you or at which critical value you are, you can write me an e-mail.
Also I'm interested in more recent data, (not only averages, but also variations) or data of other regions (Does anybody have European, African, American or World averages?).

Any new info, any astonishment, any comment: arjan675@tallpages.com