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.