Tag: average

But Why 68?

Doing mental math has been a way to avoid boredom for years, in my case. I would dream up mental math games to stay awake in classes in school and college, and often play around with number pattterns in my head when I’m out driving or riding. It doesn’t make me the world’s best travel companion, I suppose, but on the flipside, I never get bored on long solo trips.

But even in extremely short trips, such as those between different floors of the same building, I can’t help but think about math. And I’ve always wondered why lifts (elevators, if you want to be all fancy) assume that the average body weight is 68 kilograms.

Try it, the next time you get into a lift anywhere in India. Take a look at the number of people the lift will mention as the upper limit in terms of capacity, and take a look at the maximum permissible weight. The second number divided by the first will always be 68.

Why?

This question has been asked (and answered) on Quora, but the answer isn’t very satisfactory. Nor is the link used within that answer very informative. It simply states, in the case of a tragic accident involving elevators that one should assume an average weight of 68 kg, and given this assumption, it goes on to state that the accident was because of excess weight.

But that, of course, still leaves our question unanswered – why should one assume that the average weight of a human being is 68 kg?

The internet is a wonderful thing, and its long tail is a sight to behold. A Google search took me to a website that seems to be – best as I can tell – for fans of elevators. Yes, really – and they had this interesting factoid:

In Europe Standard, every passengers are assigned to at least 75 kg by default[1]. However, the suggested people can carry by the elevators are related how many spaces can the elevator allocated. Which is the Available Car Area[2]. (sic)

https://elevation.fandom.com/wiki/Capacity

That first footnote takes you to a Facebook page (of all things), and even there you’ll need to use Google Translate to get at what the text (which is in Chinese) is saying. But that just turns out to be a Hong Kong manual of some sort that simply says the same thing again. And no matter whether it is 68 kgs or 75 kgs, there still seems to be no answer to the question: why?

Wikipedia has an entry on the issue, and here is a table from that entry:

RegionAdult population
(millions)		Average weightOverweight population /
total population		Source
Africa53560.7 kg (133.8 lb)28.9%[12]
Asia2,81557.7 kg (127.2 lb)24.2%[12]
Europe60670.8 kg (156.1 lb)55.6%[12]
Latin America and the Caribbean38667.9 kg (149.7 lb)57.9%[12]
North America26380.7 kg (177.9 lb)73.9%[12]
Oceania2474.1 kg (163.4 lb)63.3%[12]
World4,63062.0 kg (136.7 lb)34.7%[12]
https://en.wikipedia.org/wiki/Human_body_weight#Average_weight_around_the_world

Note that the data is from 2005. Lots of interesting data points to ponder over in that table, not the least of which is the ratio of the overweight population to total population column – North America is at an eye-popping 74%! But the average weight, for Asia, was only at 57.7 kgs. Does that mean that we can get more people in lifts in India? Let me perfectly clear: I am not for even a single second suggesting that we carry out crazy experiments like these ourselves. But as a statistician and an economist, I cannot help but ask if there is slack in the system.

Before we move on to the next table from Wikipedia, a slight digression based on [12] in the last column of that table. That footnote refers to a paper titled “The weight of nations: an estimation of adult human biomass“, and it is quite a read in its own right. This paragraph in particular caught my eye:

The average BMI in USA in 2005 was 28.7. If all countries had the same age-sex BMI distribution as the USA, total human biomass would increase by 58 million tonnes, a 20% increase in global biomass and the equivalent of 935 million people of world average body mass in 2005. This increase in biomass would increase energy requirements by 261 kcal/day/adult, which is equivalent to the energy requirement of 473 million adults. Biomass due to obesity would increase by 434%.

Walpole SC, Prieto-Merino D, Edwards P, Cleland J, Stevens G, Roberts I. The weight of nations: an estimation of adult human biomass. BMC Public Health. 2012 Jun 18;12:439. doi: 10.1186/1471-2458-12-439. PMID: 22709383; PMCID: PMC3408371.

Back to the next table in the Wikipedia entry, however. Here is where it gets even more fascinating. This table claims that the average weight of Indians is 65 kgs – but that’s for men. Women, on the other hand, are at 55 kgs. The table is too large to paste over here, but you can click here.

So where do they get that number from? The table links to an out-of-date webpage, but a little searching around on that page takes you here.

https://drive.google.com/file/d/1j3umH5zcJAGNR_WUFwl3-0rBiemYw8DR/view

But does this mean that the average weight of Indian men is 65kgs, and that of women is 55 kgs? Or does this mean (which is what I think) that the reference Indian adult man and woman have a fixed body weight of 65 and 55 kgs respectively?

The NFHS factsheet simply tells us the percentage of people in India who are adult and overweight (30% in urban areas for both sexes, and about 20% in rural areas, in case you were wondering) – but we still dont know the average weight of Indians!

My best guess is that the number doesn’t come so much from the average weight of Indians, but rather from the nice round nature of the number itself. Now, you might not think 68 kilograms to be a round number, but try converting it into pounds, and see if my little theory makes any sense.

If anybody knows anything about this, and is willing to help, it would be much appreciated. But more importantly, to any student of statistics reading this, you can bring the subject magically alive by just looking around you, and by asking questions of a stubborn nature – such as the one that I just tried to answer here!

Just one Object

When I teach courses in introductory statistics, my focus isn’t so much on helping students memorize definitions and formulas as it is on helping them understand the point of the core statistical concepts.

I often ask a student in class to tell us about their favorite movie, for example. Let’s assume that the student in question says “Dulhe Raja”.* Ok, I might say, rate the movie for us. And let’s assume that the student says 9.

I then ask the student if every single aspect of the movie is 9/10. All the songs, all of the fight sequences, all of the dialogues, every single directorial decision – is everything a 9/10? And the usual answer, of course, is no. Parts of the movie do much worse, and there might be some that are a perfect 10. But all in all, if the entire movie had to be summarized in just one number, that number would be nine (in that student’s opinion). Which, of course, is one way to think about averages. It’s a great way to summarize, distill or boil down a dataset into just one data point.

Of course, you would want to worry about whether each dimension of the movie has been given equal importance or otherwise. Dilli-6, for example, gets a score of 6/10 from me, but that’s because the music is just so utterly fantastic. But I’m giving much more importance to the music, and not that much importance to anything else (which, for me, was almost uniformly meh). And then, of course, we start to talk about weighted averages. And this also is a great way to segue into what standard deviation is all about. Then come the formulas and the problem solving, but that’s a whole other story.

So why am I speaking about this right now? Because I read an article in The Print the other day, which asked an interesting question that reminded me of all of what I’ve written about above:

If there was a cultural artefact that truly represents everything that is India today, what would it be?

https://theprint.in/opinion/pov/rasgulla-taj-mahal-sanskrit-what-if-i-told-you-to-pick-one-object-that-represents-india/1175979/

What a question to think about, no? Read the rest of the article to find out the author’s own answer, but in what follows, I want to try and think through my own answer to this question.

First, the recognition that we’re talking about a truly multi-dimensional problem. India is diverse in terms of her geography, her languages, her dance forms, her religions, her architecture, her food, her music – I can go on and on. As, I’m sure, can you!

So should we try and come up with an artefact that covers all (or as many dimensions as possible) at once? Maybe a movie, maybe a song, maybe an epic? But can (and should) a movie or a song encompass all of what India is across space and time?

The Mahabharata, maybe? A saga told in multiple languages, in various forms, from the viewpoint of many different protagonists, interpreted in a variety of ways over the centuries, and contains innumerable references to music, dance, food, sport, architecture besides so much else.

The only other artefact that might qualify must have something to do with food. We might have different ingredients, different techniques and different methods of preparing our food, but we all love a good meal, no? So might there be a dish, or a drink, that truly represents everything that India is today?

Tea? Nimbu paani? Khichdi?

Or does this dataset have so much variance that the average isn’t really a good representation?

I haven’t yet found an answer that satisfies me – which is a good thing! – but I do think I have found a good question to teach statistics better. No?

*This is a fantastic movie, and I will not be taking any questions.